Someone or something has punched a set of rifts in the fabric of space and time, and something else is using those rifts to snatch passenger ships from the space lanes. The Doctor and Ace board one such liner, intending to allow themselves to be captured and thus discover what’s going on, but they are unprepared for the sudden violence of the attack and end up as prisoners inside an organic Ship. The robotic Ants place the ship’s passengers and crew in cryostasis and use human slaves to process them one by one, stealing their minds and storing them in Ship’s organic computer. The Doctor is able to switch off his mind to save himself from the process, but Ship’s slaves punish him for his resistance, beating him and torturing him for weeks, seizing the opportunity to take out their own fear and frustration on him. Eventually, they realise that he isn’t trying to escape -- he’s trying to rescue Ace from the cryostasis capsules. They allow him to reach her but then recapture them both and threaten to process her next. However, as they have finally been reunited, the Doctor is able to call Benny in to rescue them. Benny jumps through the time rift onto Ship, but the tortured Doctor and newly thawed Ace are too weak to help her carry them. As she tries to drag them back to the TARDIS she loses her grip, and they are all flung through the rift, scattered to various points throughout time and space.

Ace falls out of the rift in the Egyptian desert, where she is rescued from a lioness by the noble Lord Sedjet. Amused by her warrior spirit and training, he gives her a position as his bodyguard while she waits for the Doctor to show up and rescue her. But after seven months, she realises that, this time, he’s not coming back from the dead. When she is injured protecting Sedjet from bandits, he takes her off his staff and offers to make her his concubine, and she realises that he never took her seriously as a bodyguard and kept her only as a conversation piece. She departs, giving him a memento -- the force field generator which she had worn to protect her while travelling through the time rift, and which she won’t need again. But when she tries to find another position as a soldier or bodyguard, she finds that she’s outlived her novelty value. She eventually ends up working as a bouncer and waitress at a city inn, where she is found by one of Sedjet’s scribes, Sesehaten. He tells her that odd lights have been seen in the desert where she was found, and she realises that the Ants have followed her -- and that they will be seeking signs of advanced technology. She rushes back to Sedjet’s to warn him, but is too late; the Ants have already located her force-field generator and have kidnapped the entire household.

Benny arrives in France in 1798, and despite her inability to speak French she manages to locate the father of modern archaeology, Vivant Dominique Denon. He is impressed by her knowledge of ancient Egypt, and agrees to let her accompany his expedition to bring back treasures for the glory of Napoleon. While in Egypt, Benny hopes to locate the mysterious Amarna Graffito, a three-thousand-year-old message written in modern English -- which she isn’t sure existed before she arrived in France. While searching for the Graffito, she attracts the attention of cultists who worship the god Set and wish to restore him to life. The cultists shoot her and steal her diary, hoping to locate the Graffito themselves in the belief that it will lead them to their god. Denon finds and rescues Benny before she bleeds to death, and she heals herself using medical supplies she took from the TARDIS before the accident. She then leads the French cavalry to the Setite camp, where she recovers her diary and the clues she needs to locate the Graffito.

The Doctor awakens from a two-week coma to find himself in Paris, 1871, in the care of Kadiatu Lethbridge-Stewart. Paris is tearing itself apart under the disorganised Commune, and Kadiatu is stuck here with a time machine which she has only recently realised is damaging the fabric of space-time wherever it travels. The Doctor realises that the rifts which Kadiatu has punched in the Universe are irreparable; all he can do now is deal with the side-effects, such as Ship. He must also deal with Kadiatu, a genetically engineered super-soldier whose instinctive response to any threat is to enter killing mode, and with the Ants, who seem to have pursued him to Paris in an attempt to wrest the secrets of time travel from his mind. With Kadiatu’s help he escapes from the Ants and shelters with her ally, M. Thierry; however, weeks of torture aboard Ship have left him suffering from post-traumatic stress syndrome, and although he has a plan to deal with Ship, he cannot remember what this plan actually is. All he knows is that Thierry’s silent little boy is more than he seems -- and that Thierry himself is a cruel, wife-beating bully in league with the Ants, who are using the still unstable rifts to travel through Time and plunder history for valuables with which to pay the greedy Thierry for his help.

Ace and Sesehaten return to the site of the time rift, which opens as they approach, but Sesehaten pulls Ace away from it before she can leap through and escape from Egypt. He and his fellow Setites wish to overthrow the Pharaoh, Akhenaten, who has outlawed the worship of all other gods but his own; Sesehaten used to be called Sesehset before the worship of Set was outlawed. In return for Ace’s help, the priests of Set will help her to escape through the rift. Ace thus helps the Setites to kidnap Akhenaten, but she ends up talking with her captive and realises that in truth he’s no better or worse than any other king. He’s just trying to make a name for himself in history, and get his country running along efficient lines -- and the Setites are using her as a dispensable soldier, intending to rule Egypt themselves. Ace realises that she’s just striking out blindly at history for the sake of doing something, and releases Akhenaten, who understands why she acted as she did -- and reveals that her magical blue box fell out of the rift shortly after she did, and has been in his palace all along.

Ace takes the TARDIS to a prominent Egyptian monument, carves her own name in the stone and leaves the TARDIS there for the Doctor or Benny to locate in the future. First, however, she uses the console to confirm certain suspicions of hers, and once done, confronts Sesehset. The rift only opened when he approached it with her, and the TARDIS has confirmed that he is not a real person at all, but a living machine created by the Ants to help stabilise the rift. Ace forces Sesehset to take her back to the rift, and once they arrive, it opens and she leaps in. Thousands of years later, in 1798, Benny finds Ace’s graffiti, destroys it to prevent confusion amongst future archaeologists, and locates the buried TARDIS nearby. After bidding goodbye to the puzzled Denon, who is reluctant to see her go but understands that his strange visitor now has to leave, Benny sets the TARDIS to home in on the Doctor.

Thierry and Kadiatu have been allowing the Doctor to recuperate, hoping that he will come to trust them and give them the knowledge of temporal mechanics which Ship has been unable to remove directly from his mind. Thierry, however, eventually concludes that this is not going to happen and therefore uses one of the Ants’ remote controls to summon Kadiatu’s time machine to his estate, intending to use it to stabilise the rift. The Doctor, however, had sabotaged it, having assumed that the Ants would take it directly aboard Ship to learn its secrets. Thierry is killed in the explosion, but his “littleboy” turns out to be an organic machine like Sesehset, and it attempts to stabilise the rift by itself. Ace and Benny arrive at the critical moment, and Ace shoots the littleboy, preventing the rift from opening. Now both the Doctor and Ship must come up with alternate plans. Ace and Benny accompany the Doctor and Kadiatu back to Paris, where Ace learns that the Commune is doomed and will be overrun by a besieging army within days. Thousands will be slaughtered in the streets, but Ace has learned from her experiences in Egypt that it isn’t the end that matters so much as it is getting there. By fighting alongside the Commune’s defenders she can help to save a few lives, make things a little better, and pave the way for the future.

The Doctor explains to Ace and Benny that Ship is an organic computer from the distant future, built by a human colony after a disaster which had doomed the population to a slow death. To save themselves, the colonists uploaded their minds into the organic Ship -- but some of them objected to the plan, and since their skills were required, the gestalt had the Ants force them aboard Ship for processing. But when Ship left the colony it fell into one of Kadiatu’s time rifts and was damaged. It is now endlessly hunting down everybody it encounters, everywhere and everywhen, forcing them on board and copying their minds into its damaged storage units. The gestalt has filled to overflowing and the minds within have been overwritten, shattered and lost forever -- and yet Ship continues. Eventually it will die, but not until it has killed incalculable numbers of innocent travellers; and if it succeeds in stabilising the time rifts and continues to kidnap people from throughout time and space, it could destroy the Universe.

Benny discovers that Kadiatu is stealing the bodies of the dead from the Paris streets and using them as raw material with which to build more organic time machines for Ship. Ship implanted Kadiatu with an organic bug some time ago, and she has been playing for time, trying to keep Ship occupied while she develops a virus with which to destroy it. Satisfied that she has done so, she uses the virus to destroy the implant in her body, and when Ship sends its Ants to collect her she allows Ship to connect itself to her, so that the virus will destroy it. But Ship is accustomed to dealing with such threats, and it overcomes the virus and transforms Kadiatu into a component of itself. It then sends her back to Paris to kidnap the Doctor, just as Ace and Benny realise -- too late -- that the Doctor was also implanted while he “recovered” in Kadiatu’s care. The implant has now bloomed within his ganglia, and when he is returned to Ship it will be able to access his mind -- and acquire enough knowledge of temporal mechanics to stabilise the rifts.

Ace uses one of Kadiatu’s organic time hoppers to travel through the time rift to Ship, where she tries to avoid the hunting Kadiatu and track down the Doctor. Kadiatu finds and shoots Ace, but she is still trying to resist Ship’s influence and Ace is only badly wounded, not killed. Ace is too late to help the Doctor, who is already being connected to the fabric of Ship -- but the moment he accesses Ship’s central nervous system, he is able to shut it down directly. As Ship dies, Kadiatu leaps through the unstable rift into the Vortex; she could end up anywhere that the rift opens. Ace gets the Doctor back to Paris, where he allows himself to die temporarily, thus killing the organic material which Ship had implanted in him.

As the Doctor and Ace recover from their injuries, Ace reveals that she intends to stay in Paris and fight alongside the Commune’s defenders. The Doctor already knew this -- he knew where Ace would end up before she even joined him. Benny is upset, but bids goodbye to her friend, accepting her decision. Once Ace recovers from her wounds, she fights alongside the defenders of the Commune, helping to save as many lives as possible. She then sets up shop in Kadiatu’s abandoned home, intending to use the time hoppers to keep an eye on the rifts; they will never be repaired, but at least she can stop invaders from coming through. Earth has a new champion.