The TARDIS collides with a young man in a lab coat who appears to be tumbling freely through the Time Vortex. The Ship then materialises in Canary Wharf Underground station, which hadn’t yet been built in Ian and Barbara’s time; the station appears deserted, and dozens of white mice, rats and rabbits, all stamped with serial code DZ-11-B29-03, are running along the lines. The travellers hear a crash from the station’s foyer, and find that the young man they saw on the scanner has apparently materialised in mid-air and fallen to his death. The ID in his wallet identifies him as Colonel Andrews, and states that he was born in 1975; he is also carrying an envelope full of money, various denominations spanning a period of decades. The implications are that the British army from Andrews’ era is testing a method of time travel -- and that in the late 20th century, Britain will be at war.

The Doctor, disturbed by the implications of Andrews’ arrival, stays by the body with Barbara while Ian and Susan set off to find help. Barbara asks the Doctor what happens to London in her future, and when he seems reluctant to tell her, she concludes that he’s concerned that she and Ian would try to change history when they returned to 1963. She claims to have learned her lesson in Mexico, but the Doctor, who now trusts her to understand the truth, admits that travelling through history is actually far more complicated than he had originally led her to believe.

Ian and Susan hear distant explosions and realise that London is under aerial bombardment. When they seek help from a nearby hotel, a uniformed guard drives them off at gunpoint. They find an ordinary police box sitting on a traffic island, which seems to indicate that they’re closer to 1963 than they thought; even in Ian’s time, police boxes were being phased out in favour of portable radios. However, the police box contains not a telephone, but a speaking tube. Ian uses it to report finding the body, but is unnerved by the impersonal voice on the other end. He and Susan try to return to Canary Wharf station, but must circle around to avoid the man with the gun; thus, by the time they arrive, soldiers have already arrived in response to Ian’s call and have arrested the Doctor and Barbara.

Moments after the soldiers have gone, Ian and Susan see Colonel Andrews walk out the station; presumably this is a younger version of the time-traveller, who has yet to experience his death. Ian intervenes when Andrews is attacked by a crazed homeless man, but Andrews remains wary of Ian and becomes even more concerned when Ian shows him his dead future self’s identity card. Oddly, the photo on the dead man’s card is slightly different from the photo on the live man’s. Andrews decides to take Ian and Susan with him to report to his superiors, but as they make their way across the Isle of Dogs -- which appears to have been untouched by the war raging elsewhere in the city -- Ian and Susan realise that Andrews is becoming disorientated, as if this part of the city has become unfamiliar to him. Nevertheless, he eventually recognises a landmark and locates his base of operations.

Atop Canary Wharf Tower, General Bamford is watching the bombing of her city without emotion; she reacts only when her aide, Belcher, delivers a message that she’s apparently been expecting for some time. Elsewhere, an English architect named Richie Roberts has planted explosives in St Paul’s Cathedral; he then makes a cell-phone call, something that no loyal Englishman would be capable of doing. Thanks to his work, the next bombing run by the South Africans detonates the explosives and brings down the dome of the Cathedral, a terrible psychological blow to the British. Hundreds of people are killed in the collapse, but Abigail Abi, the woman who dropped the bombs, believes that the sacrifice was necessary.

The Doctor and Barbara are driven to the Byng Street Correctional Facility, where the Doctor pretends to be distracted and confused -- until it becomes clear that elderly vagrants can be shot without trial. A scientist named Kelly interviews the newcomers, and they learn that the date is 24 June 2006; England is at war, and anyone who can’t contribute directly to the war effort is to be executed. The Doctor claims to have an envelope containing money from different eras, and Kelly concludes that the Doctor and Barbara are time-travellers from the future who have come back to see his work. He thus has them released and takes them to his base of operations, where several lab technicians are working on a large hoop that seems to disturb the Doctor. Here, they are reunited with Ian and Susan, and with Colonel Andrews -- but not the same Andrews whom they found dead at Canary Wharf station. There are in fact about half a dozen different versions of Colonel Andrews in the mess hall...

The Doctor demands to know the details of the experiment, and Kelly and the Andrewses explain that the project was developed using alien technology found on Earth in the 1960s. Before sending through Andrews, they sent through a white rabbit marked with serial number DZ-11-B29-03; however, it was a toss-up between sending a rabbit or a rat, and the choice was made at the last moment. Before they could send Andrews through, other versions of Andrews began walking into the laboratory, each with different memories, as if they’d come from different versions of history. Kelly explains that the portal was supposed to act as an anchor, to ensure that the time-traveller arrived at the correct point in space as well as time -- but for some reason, these versions of Andrews have been appearing elsewhere on the Isle of Dogs, such as the Canary Wharf Underground station.

General Bamford arrives at the lab, and is apparently unnerved by the sight of the hoop; however, she pulls herself together and demands to know why Kelly has had prisoners released from Byng Street. She agrees to let the Doctor remain when it becomes clear that he has useful scientific knowledge, but orders that his companions and the duplicate Andrewses be sent back to Byng Street -- and orders her troops to search Canary Wharf station for anything unusual. One of the scientists, a timid man named Griffiths, offers to interrogate the prisoners, and Bamford agrees to let him do so. Ian tries to give his guards the slip, but Griffiths stops him, telling him privately that this is not the time. However, while speaking to the guards, Griffiths lets slip within earshot that the prisoners are to be executed after their interrogations.

On the way back to Byng Street, it becomes clear that there are small but significant differences between each version of Andrews; this is not merely the same man at different points in his life. Susan admits that history is more complicated than the Doctor had led his human companions to believe, and she and Griffiths compare notes and theories about what would happen were it possible for a person to go back and change history. To Griffiths’ alarm, Susan suggests that multiple versions of Andrews will continue to appear for as long as the experiment keeps running -- and that the resulting build-up of temporal energy, caused by the bottleneck in reality as the different versions struggle to break through, could destroy the entire planet.

In Kelly’s laboratory, the weary Bamford admits that the war with the Afrikaans is going badly; the only reason the Isle of Dogs has been spared bombardment is that a stray hit on its nuclear reactor could devastate even the Afrikaans’ European allies. She demands that Kelly demonstrate his work, and seems mesmerised when energy begins to pulse through the hoop; however, the Doctor prevents her from stepping through it. To his distress, he realises that she intends to use this technology as a weapon, even if it means destroying the world in the process. A soldier then announces that an unusual police box has been found at Canary Wharf station, and as if she’s been waiting for this news, Bamford orders her men to bring it to the labs for study. All attempts to break into the TARDIS fail, and when more Andrewses begin to materialise next to it, Bamford orders Kelly -- much to the Doctor’s distress -- to put the police box through the hoop.

At the Byng Street facility, Griffiths questions Barbara and Ian separately. Realising how dangerous their position is, particularly if they’re caught out in a lie, they decide to stick to the truth. When Griffiths learns that they are from 1963 and are unaware of the history of the past 40 years, he asks Barbara if she’d be tempted to change the future should she ever return home. Dissatisfied with her inability to answer, he warns her that the Isle of Dogs has long had a problem with vagrants, and that the penalty for vagrancy is death. He then questions Ian, but after he leaves to report to Bamford, Ian realises that he’s left the door open. Searching for Barbara, Ian instead finds the dead bodies of six Andrewses, all of whom have been shot in the head. He then finds a trail of threads that Griffiths has planted in the corridor, leading him to the interrogation room where Barbara and four Andrewses are awaiting interrogation. Ian overpowers their guard and reveals what he’s seen; horrified, the Andrewses agree to help them escape.

Armed with the guard’s gun, Ian, Barbara and the surviving Andrewses rescue Susan and return to the lobby; there, Ian fails to bluff his way past the guard, and one of the Andrewses shoots the guard dead. More soldiers catch them trying to escape and open fire, killing two of the Andrewses; the others barricade themselves in the building, and Ian manages to convince the staff of the facility that enemy soldiers have attacked the building. In the ensuing confusion, the time-travellers head deeper into the facility, as Ian believes that Griffiths engineered their escape and must have set up a way out. Bamford takes charge when she hears of the attempted break-out; unaware that Griffiths is responsible, she concludes that Ian must be a trained South African spy, and orders her men to shoot him on sight.

Ian and the others find Griffiths’ intended escape route and flee in an armoured car parked by the exit. Believing that it’s too dangerous to return to the laboratory, and unaware that the TARDIS has been moved, Ian drops off the others at Canary Wharf station to wait while he rescues the Doctor. Back at the laboratory, he discovers his mistake, and when he tells Kelly and the original Andrews that the duplicates are being executed, the shocked scientists set off to confront Bamford. Unfortunately, in doing so, they let slip that Ian is back at the lab, and Bamford sends a young soldier named Sharrock to execute him. Meanwhile, the Doctor activates the time portal in an effort to understand how it works, and Ian, mesmerised, nearly steps through the hoop. Before he can do so, Sharrock enters the lab, forces the Doctor to switch off the hoop, and prepares to shoot Ian -- but another version of Ian bursts in, tackles Sharrock and throttles him to death. Sharrock shoots the alternative Ian as he dies, and the original watches helplessly as his counterpart -- who is wearing a wedding ring -- dies trying to pass on a message to Barbara. The Doctor tells the shocked Ian to hide in the TARDIS, intending to let the soldiers believe that the dead Ian is the original.

Bamford makes no secret of the fact that she’s having the duplicates killed without trial, and threatens to do the same to the “real” Andrews if he protests. She orders Kelly to shut down the experiment and leaves to get some rest, but then another Andrews materialises next to the TARDIS -- and, upon seeing Griffiths, accuses him of working for the Afrikaans. Griffiths laughs off the accusation, but the Doctor picks his pocket and discovers that he’s carrying a mobile phone. Griffiths drops the pretence of being a bumbling, absent-minded scientist, and pulls a gun on the Doctor -- but before he can shoot, Bamford unexpectedly walks into the room and overpowers him. The Doctor convinces her to interrogate Griffiths rather than just shoot him on the spot, but as she goes to set up the court-martial, the puzzled Kelly wonders why she returned so quickly. The Doctor suspects the truth, but only Ian, hiding inside the TARDIS and watching events on the scanner, has seen for himself that this version of Bamford appeared out of thin air, just like the alternative versions of Andrews.

While waiting for the Doctor and Ian to return, Barbara speaks to one of the Andrewses and is unnerved by the social changes that he accepts as a part of his history. Susan enters the station to find that the TARDIS has gone, and one of the Andrewses, who’d been unaware until now what they were waiting for, claims that it’s in the lab and that the Doctor is showing Kelly how it works. They are then recaptured and taken back to Byng Street, where the soldiers cruelly inform Barbara that Ian has been killed and show her his body. Numbed by the shock, she finally admits to herself that she loved him, and gives up all hope of rescue from this terrible place. The soldiers have orders to execute them all, but they’ve been killing the duplicate Andrewses first, and as more and more duplicates keep appearing, Susan and Barbara are moving further down the list. As they wait, they see the Doctor being escorted by soldiers -- but he’s here to interrogate Griffiths, and he does not respond to his companions’ presence in the facility. For the first time, it occurs to Susan that, due to the dangerous time experiments, her grandfather may now have higher priorities than saving her life.

The original Andrews catches Ian when he decides to risk emerging from the TARDIS, but the knowledge that his other selves are being executed has shaken him, and he convinces the soldiers that Ian is merely one of his colleagues. He and Ian also convince the soldiers that Ian must return to Byng Street in order to requisition spare parts for the time portal. More duplicates of Andrews continue to materialise next to the TARDIS, and the soldiers continue to take them away to their deaths; however, the original Andrews manages to get some of his duplicates to a place of safety before the soldiers can catch them. Meanwhile, in France, the Afrikaans are preparing to launch their final assault on London, and despite the danger, Abigail Abi has insisted upon joining the invasion force.

The Doctor questions Griffiths, who claims to be a freelance mercenary who infiltrated Kelly’s programme in order to sell its secrets to the South Africans. He also claims that he never got the chance to do so, but he’s lying. Before the court-martial begins, the Doctor speaks with Kelly, who is surprised to learn that the Doctor is unfamiliar with the Machine that tried to take over the world by hypnotising people via radio transmissions. The Machine was destroyed in 1969, but the weakened survivors of the battle turned on each other, and the world was further devastated by the ensuing wars. Telephones and other broadcast media were outlawed, which is why possession of a cell phone identified Griffiths as an enemy agent. The court-martial begins, and Bamford sentences Griffiths to death without giving him a chance to defend himself -- but before he can be removed from the courtroom, another Bamford arrives, having just learned that this court-martial is taking place. Earlier, the Doctor prevented Bamford from stepping through the hoop; the Bamford who just presided over the court-martial is from another version of history in which he did not. Too late, the Doctor realises from the duplicate’s resigned behaviour what’s going to happen, and he is unable to prevent the original Bamford from having her troops execute the duplicate for being an aberration from the true version of history.

Ian bluffs his way past the soldiers at Byng Street and knocks out the soldier guarding Barbara and Susan. He explains that the Ian they saw dead was a duplicate like the other versions of Andrews, but Barbara, still in shock and mourning for her Ian, sees the unconscious guard and refuses to accept that her Ian could be so violent. She has little choice but to flee with him, but intends to denounce him as an impostor. They rescue Griffiths from his executioners and escape from Byng Street, and Griffiths leads them to Canary Wharf Tower, bluffs his way past the receptionist and takes the others to Bamford’s suite on the top floor. There, he overpowers Belcher, possibly killing him, and then sets Bamford’s flat on fire, sending smoke signals into the sky over London; since his cell phone was confiscated, this is the only way he can contact his allies and inform them that they can begin the invasion.

Having executed her counterpart, Bamford now orders Kelly to put the TARDIS through the hoop. The Doctor realises that Bamford knows more than she’s saying, but before he can find out what, Afrikaans paratroopers descend from the sky and attack. Unlike the English, who fear technology due to their experience with the Machine, the Afrikaans have traded with the machine people from the South Pole and have acquired energy weapons against which the English have little defence. The Doctor urges Bamford to surrender rather than send her men to their deaths, but she orders her troops to fight to the last man, sends a soldier named Skinner on a particular mission, and takes the Doctor and Kelly back to the laboratory to put the TARDIS through the time portal before the Afrikaans can capture the building.

Griffiths is finally reunited with Abi, but seems strangely distant towards his old friend. Barbara sympathises with Abi’s distress at Griffiths’ behaviour, but then the 1960s woman makes an unthinkingly racist comment regarding Abi’s country of origin and the mood sours. The invaders are soon in need of a field hospital, and Ian suggests setting up in Canary Wharf station -- but the English attack them there, throwing grenades in amongst the wounded. In the brief and bloody battle that follows, Barbara stabs an English soldier to death to save Susan’s life, and Skinner and his men slip past the fighting and into the Underground. Griffiths spots them and realises that they intend to sabotage the nuclear reactor. Abi and her commander, Wu, set off after them, while Griffiths, Ian, Barbara and Susan return to the lab to confront Bamford and rescue the Doctor.

The Doctor tries to stop Bamford one last time, but fails, and she sends the TARDIS through the time portal moments before the Afrikaans arrive and seize the lab. Bamford holds them off at gunpoint, scorning Griffiths’ apparent belief that he can build a better world with “lies and aberrations.” The Doctor has by now realised the truth, and when he asks her where she was when Kennedy was shot (a question that comes as a surprise to Barbara), Bamford is unable to answer. Even though she’s clearly in her 60s, she hadn’t yet been born 43 years ago. Bamford is also a time-traveller, from a different version of 2006; this is why she hates Andrews and the duplicates so much, as they remind her that her home, the version of history she regards as true, has vanished forever. Bamford admits that she travelled through Time and materialised on West India Quay on 17 October 1972; however, she also claims that she’s set all of these events in motion by sending the police box through Time, as it will be studied by the scientists who use it to create the time portal in the first place. She then tries to shoot Andrews, to prevent him from ever stepping through the time portal in the first place, but Griffiths shoots and kills her first.

The Doctor explains that the presence of the TARDIS has thrown the experiment into disarray. The portal itself was supposed to act as an anchor, but since the TARDIS is a much more powerful lodestone, time-travellers from several different futures have been drawn to it and thus to the current timeline. Griffiths had already claimed that the Isle of Dogs had a problem with vagrants; since Bamford has sent the TARDIS into the past, presumably many of the vagrants are time-travellers who were drawn to its presence and trapped in a past that was not their own. Barbara has noticed Ian trying to hide his other self’s wedding ring, and has realised the implications; he really is her Ian, and the other Ian’s death means that there’s another version of herself out there who is now a widow -- unless that version of history no longer exists. She now understands more of the dangers involved in trying to change history, and the Doctor admits that there’s another complication; changes on this scale could attract attention from the wrong sorts of people. Even if this business is resolved safely, he fears that Susan will no longer be safe travelling with him.

Wu, Abi and their squad kill most of Skinner’s suicide squad with their energy weapons, but Abi is shot and killed by a sniper at North Greenwich station. Wu and his men arrive at the reactor too late; Skinner has shut himself in the control booth, and loyal English scientists are giving their lives to hold the Afrikaans back while he lowers the control rods. Wu contacts Griffiths and asks him to send reinforcements, but despite the Doctor’s and Susan’s best efforts, they are unable to narrow the portal’s focal length and the soldiers who step through the hoop fail to arrive at the reactor. Wu and his men break into the control booth too late, as Skinner lowers the control rods, triggering a nuclear explosion. However, the Doctor and Susan configure the time portal to draw energy away from the explosion, and use it to stabilise the portal. There will still be some damage and dangerous fallout, but the Doctor can now use the time portal to travel back to 17 October 1972, contact the original version of Bamford when she arrives, and perhaps stop her before her actions lead to this devastating version of 2006. The Doctor finally admits to Barbara that he lied to her in Mexico; it is possible to change history -- indeed, they do so every time they step out of the TARDIS -- but he can’t bear to sit aside and just watch when he could be out in the thick of things himself.

Griffiths volunteers to accompany the Doctor and his friends in order to put history right, although this means abandoning his own daughter; he had always intended to do so, which is why he was so distant to his old friend earlier. Also sickened by the war, Kelly gives the Doctor the address of the labs where the experiments first began; however, he and the multiple Andrewses decide to remain, even though they’re unsure whether this version of history will continue to exist if the Doctor and his companions change the past. Griffiths and the travellers step through the hoop, and with the Doctor’s help, they keep hold of their identities despite the disorienting trip through Time -- and successfully materialise on West India Quay, 34 years earlier.

Though surrounded by hostile and suspicious vagrants, the travellers find shelter in a run-down building on the quayside. The Doctor, Ian and Susan stay in the shelter while Barbara and Griffiths leave to find food and learn the date. According to Griffiths, if this is 1972, then the Machine has recently been destroyed -- but the countries of the world have divided into tribal city-states, paranoia and suspicion are rife, and in Britain, minorities are soon going to be rounded up and imprisoned. He and Barbara are attacked by two vagrants, a man and a woman, and although Griffiths kills them in self-defence, he notes that the man was wearing the remains of a lab coat; as the Doctor had suspected, the vagrants are time-travellers driven mad by their isolation in a history that is not their own. Barbara and Griffiths buy gruel and potatoes at a nearby market, and return to the quay with a tattered newspaper identifying this as 15 October 1972; there are many competing newspapers in London, all jingoistic and politicised, further evidence that the country has descended into anarchy.

Ian and Griffiths keep watch during the night, but despite their grim surroundings, Susan remains optimistic and enthusiastic. The Doctor sees another time-traveller materialise on the quay and notes how easily the vagrants accept the dazed man into their community, which may explain why he and his friends have not been attacked. He also notes approvingly that Griffiths can take care of himself; perhaps he would make a good match for Susan. Griffiths promises to take care of her if necessary, haunted by memories of his own eight-year-old daughter -- who may now never exist because Griffiths is changing the past.

Unaware that her grandfather is deciding her future, Susan convinces Ian and Barbara to go looking for the future location of the laboratory, but on the way, Barbara notes that Ian is haunted by the death of his other self, unsure whether he could have become that man if he’d done things differently in his own life. Before he can show Barbara the other Ian’s wedding ring, however, they hear Susan scream, and arrive just in time to see an elderly vagrant running away. Susan seems unharmed, but is badly shaken by the encounter, and accompanies Ian and Barbara back to the ruined building without protest.

The next day, 17 October, the young Bamford arrives on schedule, and the Doctor and his companions are there to greet her. Though disoriented by her trip through Time, she is quick to grasp that something has gone wrong; however, unlike her intransigent future self, she is young and optimistic, and willing to listen to the others. She agrees to accompany them to the site of the early time experiments, but notes that there’s someone else she’d like to look up while she’s here. The party sets off through Wapping, but it’s a dangerous trip, as gangs roam the battle-torn streets and strangers are regarded with suspicion. The travellers stop in at a pub for food, but are attacked when Bamford reveals that she’s carrying money; fortunately, the brawl breaks up when one of the men attacking her sees that the money has a picture of “King William” and dismisses it as counterfeit. Despite the risk that two smaller groups will present easier targets to the gangs, however, Bamford still wants to take a detour, and the Doctor advises Ian and Barbara to accompany her.

Ian, Barbara and Bamford encounter a dazed homeless woman whose mind was destroyed by the Machine, and Ian and Barbara are surprised by the tenderness Bamford shows towards the unfortunate woman. However, Bamford receives an unpleasant shock when they reach their destination, an inner-city hospital; the woman she came to meet, a paramedic named Karen Baldwin, was killed on ambulance duty when vagrants tore apart her ambulance, looking for food. Stunned, Bamford reveals that Karen was her mother, or should have been -- but as Karen never even met Bamford’s father until 1975, this means that Bamford is now in a version of history in which she will never be born. As Bamford tries to come to grips with this, Ian realises that they’ll have to sell his other self’s wedding ring for cash, and he finally accepts that he and his other self are two different people and that he shouldn’t feel constrained by his other self’s choices. Seeing this gives Bamford strength, and when Ian and Barbara take her to a nearby pub to recuperate, she pulls herself together for their sake and decides to make a new life based on who she is here and now. Ian and Barbara realise that, without them, Bamford would have fallen apart and become the hardened woman they first met.

The Doctor, Susan and Griffiths visit the laboratories in Whitehall where the younger Kelly and his supervisor, Townsend, are studying the alien artefacts that will eventually be used to create the time portal. The Doctor gains access to the labs by showing them Griffiths’ mobile phone, evidence that he and his friends are travellers from the future. However, he then finds that the scientists are studying not the TARDIS, but artefacts of Dalek origin, recovered from a school in East London. The Doctor and Susan trick the scientists into letting them wire up the alien artefacts together; however, instead of demonstrating how to use them, the lash-up vanishes from the laboratory, putting an end to the experiments for good. Without an anchor, the alien artefacts will materialise in the heart of the sun and be destroyed. The Doctor, Susan and Griffiths escape from the enraged scientists, but when Susan stops Griffiths from killing their pursuers, he finds himself ashamed to realise that his friends’ morality is better than his.

The travellers now have another problem to deal with; since the TARDIS wasn’t at Whitehall, it must be somewhere else -- and since the older Bamford recognised it as a time machine, that must mean that her younger self encountered it somewhere. But when the Doctor is reunited with Ian and Barbara, he learns that they’ve changed Bamford’s future through their acts of kindness. Though he sympathizes with Bamford, he must now inform his companions that without their intervention, Bamford would have found the TARDIS -- and since they have changed her future, they may all end up stuck here. Nevertheless, Griffiths and Bamford -- who now asks her friends to call her Louise -- decide that they’ll make the best of their life here, and try to change the future for the better by giving people hope and appealing to their better nature, rather than dividing them through fear of the unlike. The travellers return to the Isle of Dogs to ponder their future, but then encounter the elderly tramp who confronted Susan the day before. Before Ian can drive him off, however, Susan admits that the tramp didn’t attack her; he was just trying to speak to her, as he recognised her. The tramp is an elderly version of Ian.

The elderly Ian reveals that he stepped through the hoop in order to escape from soldiers who wanted to execute him, and ended up materialising in mid-air and falling into the Thames in 14 July 1948. Trapped in the past with no identification, he was arrested for vagrancy, and by the time he was released he had become a shell of his former self, unable to communicate clearly when he encountered his younger self in 1962. He lived through the rise and fall of the Machine, and when he spotted Susan and his own younger self the other day, he finally realised that he too was a temporal duplicate like the Andrewses. Nevertheless, he is able to pull himself together and communicate what he was trying to tell Susan: he saw the TARDIS underwater when he fell into the Thames in 1948. It’s still there, beneath the quay, where it’s been drawing test pilots off course for decades. Presumably, had Ian and Barbara not saved Bamford with their act of kindness, the traumatised woman would have encountered the elderly Ian and thus found the TARDIS.