London, 1346. A mad old friar has been drawn to the city by the memory of voices in his head, seeking the strangers who have recently arrived in London. They have fought a war and lost, and have been exiled from their home; but their corporeal hosts died while travelling through the null-dimensions, and they must find new hosts amongst the people of this world. But as they scan the surrounding time-stream, they find that the world will soon be struck by plague and one-third of the population will die. They do not have the energy to leap to another world; they do not have the energy to keep leaping from host to host as the plague kills them off; and they cannot retreat to the null-dimension, as their new hosts from this world cannot survive there. Their exile is a death sentence. They have only one hope; their scan of the time-stream indicates the presence of a man named Roger Bacon, in the direction known to these people as the "past", who conducted some initial research into distilling an elixir of life. They must send one of their own back to encourage his researches, so that the people of this time period will have a defense against the plague.

Two thousand years later, Nyssa of Traken is teaching at a university, trying to ignore the faculty politics which are complicating her life and the threat of war looming over the system. After completing her work on Terminus, Nyssa roamed the galaxy seeking causes to fight for, but came to realise that she was fleeing from her own feelings; and when she failed to prevent a holocaust on the planet Exanos, it all became too much for her to bear. She thus retreated to this quiet teaching position, and in order to distract herself she has plunged into work on a thesis, using her first-hand experience of Earth's past to prove that 13th-century philosopher Roger Bacon was the true pioneer of the scientific method. But one day she wakes to find that all of her research is changing -- her thesis is now, and always has been, about the engineer Brunel. The TARDIS then materialises in her Home, bringing with it an earlier version of the Doctor she knew, one who has yet to meet her; he is on the trail of a historical anomaly, and for some reason his ship has brought him here. His presence reminds Nyssa of a vague feeling that something was wrong with her research; the sheer volume of work she has done enables her to retain vague memories of the past as it was before it changed. The Doctor thus determines that the anomaly has something to do with Roger Bacon, and decides to go back to 13th-century Oxford to investigate further. Weary of faculty politics and the threat of war, and longing for a simpler time and place like her childhood home on Traken, Nyssa slips aboard the TARDIS when the Doctor isn't looking, and accompanies him back to Oxford in the year 1278 AD.

The knight Richard of Hockley arrives in Oxford to take command of the castle garrison and keep the peace between the different factions in the town. He will be staying at the castle of the lady Matilda, his lord's aunt, and is to consider himself under the orders of the university chancellor, Philip of Seaby. His first task seems simple enough; he is to find two buskers who are using prisms to demonstrate the principles of reflection and refraction, and expel them from the town. He's expecting to find a couple of scruffy ne'er-do-wells, but that is not the case -- the man who calls himself the Doctor is clad in bright, well-tailored clothes, and his assistant Nyssa is a courtly noblewoman, fairer of face and bearing than any woman Richard has ever met before. As he tries to decide what to do, a messenger arrives from the university; Brother Godwin, who had gone missing the night before, has been found dead.

The Doctor, who had been conducting his street performances in the hope of attracting Bacon's attention, follows Richard to the university. There, the friars try to bar them from entering, claiming that this is an internal matter. The Doctor claims to have been invited personally by Roger Bacon, and to his surprise, Bacon's constant companion Brother Thomas confirms that this is indeed the case. The Franciscan minister, Hubert, has little choice but to let the Doctor enter, but he will not permit a woman inside. Richard thus offers to arrange for Nyssa to stay with the lady Matilda, and she accepts his offer, assuring the worried Doctor that she can take care of herself. The Doctor in turn promises to keep Richard informed about his investigation into Godwin's death. Richard seems somewhat tongue-tied around Nyssa, but she's too tired to think about it, and simply accompanies him to the castle, unaware that he is trying desperately to think how to woo and win her.

Hubert assigns the proctor, Alfric, to investigate Godwin's death; he must try to prove that it was an accident, or if possible find evidence to implicate Bacon. Somehow the Doctor takes over the investigation, and he points out odd discrepancies at the alleged scene of the death. It seems that Godwin slipped while drinking alone in the wine cellar and hit his head against a barrel tap, but there are marks on the ground which indicate that something heavy was dragged into the cellar. There appears to be no reason why Godwin would bother to both lock and bolt the door -- but on the other hand, if he was killed elsewhere and the body moved, how did the killer bolt the door from the inside? The Doctor suggests that Alfric examine Godwin's body for scuff marks and to determine whether more than one blow was struck to his head. This is indeed the case; Godwin was murdered. Hubert, acknowledging the Doctor's intelligence, is plain with him; rival brotherhoods such as the Dominicans would love to expose heresy amongst the Franciscans, and the troublesome Roger Bacon is a great liability to their order. As is the Doctor, who is still an unknown quantity. The Doctor assures Hubert that he's not here to cause trouble, but to steer Bacon away from such pursuits as astrology and alchemy, and Hubert, satisfied, decides to permit the Doctor to speak with Bacon tomorrow. Thomas is also satisfied when informed; perhaps this Doctor will give Bacon the help he needs to complete his work. He hasn't been doing well on his own despite all of Thomas'... encouragement.

Morning dawns bright and beautiful over Oxford and the garden of peace that Matilda's castle has become. This is just what Nyssa has been looking for, a place to forget her cares and lose herself in the tranquility of the gardens; the only intrusion here is Richard, a coarse and unmannered warrior who reminds her of everything she's trying to leave behind. Richard in turn remains flustered and lovelorn around Nyssa, and Matilda's transformation of the castle from a fortress of war into a garden of love seems only to highlight his inadequacies as a courtly suitor. Matilda senses the reason for his distress, and, seeking to make her castle an idyll of true love, she determines to help him win Nyssa's heart. The chancellor then arrives to speak with Richard, and Nyssa excuses herself when talk turns to the death of Godwin. As it happens, Godwin was one of two friars who secretly kept the chancellor informed of the goings-on in the brotherhood; perhaps he was killed because his role had been discovered, or perhaps his fellow informant, Oswald, killed him in one of their frequent quarrels. In any case, the friars are bound to be keeping a closer watch on their own now, and the chancellor will have trouble getting word from inside. As Oswald is known to be an expert gardener, Matilda offers to summon him to the castle, to advise on the upkeep of her gardens... and to deliver secret messages to Richard.

Alfric accompanies the Doctor to his meeting with Bacon, where Thomas keeps a watchful eye on them as the Doctor and Bacon discuss the friar's past researches. Bacon still keeps notes on optics and a cache of magnetic lodestones in his cell, and he has even invented the telescope centuries before Lippershey, but despite this he insists that he put all these things behind him when he joined the Franciscan order. He has devoted his life to prayer, preaching, and the occasional lecture. The Doctor, fascinated, decides to attend Bacon's lecture at the Italian school later that day. As he and Alfric leave, Alfric, realising that he needs the Doctor's help, admits that Hubert has told him to look for evidence implicating Bacon in the murder; Hubert suspects that Bacon has been conducting illicit research, and wishes to deal with the matter internally before a rival brotherhood can use it to embarrass the Franciscans.

The Doctor realises that Thomas is following them, and sends Alfric on ahead so he can speak to Thomas privately. Thomas admits that Bacon is indeed conducting research, and asks the Doctor for his help. When the Doctor promises to give it, Thomas helps him in turn by suggesting that Alfric is the killer; Godwin was overfond of the wine cellar, and Alfric may have disposed of him to save the brotherhood embarrassment. The Doctor finds this implausible -- and how did Thomas know Godwin had been murdered, when that fact has not yet been made public? He rejoins Alfric, who has used the Doctor's methods to recreate the night of the murder and has found a staff marked with blood in the quiet shelter by the wall. From this vantage point, one can see the islands and islets of the Thames, including one which was owned by Roger Bacon before he joined the order and gave up all personal property. The old observatory on the islet has been abandoned for years... in theory. If Bacon is still conducting heretical research, perhaps Godwin saw someone leaving the observatory, and was murdered for it.

The Doctor attends Bacon's lecture, at which the old man delights in offering up controversial and scandalous theories. The Doctor takes just as much delight in provoking him even further, inciting a near-riot amongst the scholars. Thomas, however, is concerned to note that Alfric is not there, and he slips away, fearing that Alfric is taking the chance to search Bacon's cell. In fact, Alfric has crossed over to the observatory, where he finds new, freshly oiled bolts on the outside of the building, as if meant to keep someone inside. The observatory is deserted, and Alfric finds that the vast library of books inside -- a wondrous storehouse of human knowledge -- is crumbling to dust, all of the volumes illegible under the rot. There is evidence that Bacon was still writing new theses in 1266, almost a decade after he joined the order -- but that was over 12 years ago, and although it proves that Bacon joined the order simply because their land was next to his observatory, all of the other evidence suggests that he did indeed give up his work long ago. Almost all. One desk is clear of dust and grime, and is covered with distillation equipment and papers which indicate that Bacon is trying to create an Elixir of Life. This is all the proof Alfric needs; Bacon is meddling with alchemy, and the Franciscans will punish him themselves, locking him up for the rest of his life.

Alfrid returns to the friary, unaware that he is being observed. Brother Oswald is sitting by the river, mourning Godwin's death; he and Godwin were lovers, and they joined the brotherhood so their close proximity and lack of interest in women would not be considered suspicious. But the chancellor found out their secret, and blackmailed them into becoming his spies within the order; thus their love turned sour, and Godwin turned to drink. Oswald, fearing that Godwin would say something he shouldn't while under the influence, fought with him on the night of his death; now, he has heard the Doctor and Alfric discussing their pursuit of a killer, and fears that he will be suspected of Godwin's murder. However, he still has his duty, and when he sees Alfric returning from the observatory with papers, he follows, hoping for news to report to the chancellor. Thomas is on the roof, using Bacon's marvellous reflective lenses to observe the goings-on in the town, when he sees Alfric present Hubert with the papers about the Elixir of Life. This is disastrous; not only has Thomas lost years of Bacon's valuable work, but Hubert will now be able to lock Bacon up and prevent him from completing his research. Thomas must recover the papers, whatever the cost...

That night, Hubert fails to attend dinner after vespers, and when Alfric investigates he finds that Hubert's cell has been ransacked and the papers stolen. Hubert shows up the next day -- dead in the Jewish quarter, his body circumcised and a sign draped around his neck proclaiming death to the oppressors of the Jews. Richard and his men quell the angry mob before a riot can erupt, and the Doctor points out that circumcision is a holy ritual which would not be used on an enemy -- and that the note around Hubert's neck was written in Latin, rather than in Hebrew or English. Hubert must have been killed by a fellow friar, and the body moved to the Jewish quarter to cast suspicion on them. But as long as the real culprit remains unidentified, the Doctor is only too aware that the townspeople's hatred for the Jews will not diminish.

Richard returns to the castle, having just missed Oswald's visit. Urged on by Matilda, he bids Nyssa good day, but once again he stumbles over his words; in vowing to protect her, he only distresses her with the news that there is a killer on the loose. Cursing his clumsy speech, he tries to make things better by giving her his knife so she can defend herself when he is not there to protect her. This distresses her further, and as Richard retreats, tongue-tied, the shaken and angry Nyssa leaves his knife in the bower, refusing even to look at it.

The Doctor and Alfric question the friars, to see who cannot account for their activities at the time of Hubert's murder. Most were attending vespers at the time, but the chief suspects, Oswald, Thomas and Roger Bacon, were all absent. When the Doctor and Alfric arrive at Bacon's cell to question him, they find Thomas shouting at him; Bacon seems to be taking the loss of his papers with equanimity, despite Thomas' fury that the hope of making an Elixir has been lost. When questioned, Thomas claims that Roger was ill yesterday and that Thomas stayed with him; but Roger looks relatively hale and hearty now. On another matter, the Doctor inquires after the donkey cart which Thomas used to transport Roger to the Italian school the other day, and Thomas claims that it was stolen while he was inside. The Doctor and Alfric then question Oswald, who seems terribly nervous and also claims implausibly to have been ill during vespers. Alfric returns to his chambers to ponder what he's learned, only to find that they have been ransacked. He tells the Doctor about the papers, and the Doctor deduces that someone is trying to recover them -- someone who murdered Hubert when he was found searching his rooms. Alfric seems to have escaped a similar fate, but the fact that his rooms were searched implies that the killer did not find the papers in Hubert's room. Which means that someone else has them.

That night, the nervous Oswald builds a barricade of furniture against his door to save himself from further questioning -- and it saves his life when someone determined and strong tries to break in. Oswald spends a sleepless night holding the door closed against his attacker, and when dawn breaks he heads for the castle to attend Matilda and unburden himself. Someone has torched a Jewish home during the night, apparently indicating that they are still blamed for Hubert's murder. At the castle, Richard tries and fails once again to profess his love for Nyssa; she cares for him in a way, but he is too much a warrior when all she wants from life is peace and solitude. Richard speaks with Oswald, who returns to the friary unburdened, passing the distracted Thomas on his way back. Meanwhile, Matilda goes into town to attend church, and Richard sends the garrison with her as an escort; he will join them later, after attending the chancellor with his news. He really should go at once -- but from his vantage point in the castle he can see Nyssa resting in the bower, and he sets to work composing a love letter.

Thomas has seen the Doctor and Alfric heading for the observatory, and has taken steps to deal with them. The Doctor is awed by the evidence of scholarship in the observatory, but knows he has a responsibility to history. Can he bear to leave these papers to rot? The decision is taken out of his hands when someone bolts him and Alfric into the building and sets it afire; fortunately, the Doctor is able to use one of Bacon's lodestones to draw back the bolts from the other side, and he and Alfric escape. Alfric now understands how Godwin was found in a room apparently bolted from the inside... and only Roger Bacon has a collection of lodestones. But he is too old and frail to lift them to the height of the deadbolts. When the Doctor and Alfric confront Bacon with evidence of his heresy, he admits that he joined the Franciscan brotherhood only for food and shelter, after expending his entire fortune on his researches; but over the years, he has come to appreciate the life of poverty and prayer. It is Thomas who forced him to resume his researches into the Elixir of Life, beating and scourging him when he tried to resist.

There is no sign of Thomas in the friary, although Oswald claims to have seen him while leaving the castle. Before searching for him, the Doctor and Alfric report to the chancellor that they have found the killer. Godwin must have seen Thomas leaving the observatory; only Thomas could have used lodestones to bolt Godwin into the wine cellar; he would have known that the papers had been taken, he knew Godwin was murdered before anyone had said so in public, and he "lost" a donkey cart capable of transporting a body, on the day that Hubert's body was transported to the Jewish quarter. The chancellor admits that Godwin and Oswald were his spies, and that Oswald's visits to Matilda's castle are pretexts for him to pass on information to Richard. The Doctor is appalled by the implication. Oswald must have taken the papers. Thomas, who has killed in pursuit of the papers already, saw Oswald leaving the castle empty-handed. Thomas is not in the friary... and Nyssa is in the castle.

Richard, busy working at his love letter, pays little attention when a Franciscan friar enters the room behind him... and is thus entirely unprepared when Thomas stabs him and takes back the papers. Hearing Nyssa approach, Thomas cuts Richard's throat so he will be unable to speak, and hides as Nyssa enters the room to find Richard dying. When Richard finally does die and Nyssa leaves the room, Thomas emerges from hiding, only to find that Richard has written the name of his killer in his blood. Nyssa retreats to the bower, unable to deal with the violent death, but Thomas pursues her to silence her. She now knows there will never be sanctuary for her anywhere, and welcomes death; but the voices in Thomas' head, the ones which tell him what to do, urge him to leave her body with Richard to make it appear that she killed him and then took her own life. As he tries to drag Nyssa from the bower, she makes her choice; the knife which Richard left for her is still here, and to Thomas' surprise, she grabs it and stabs him in the head. The Doctor and Alfric arrive to find that Nyssa has chosen to live.

When Thomas wakes in the infirmary the voices in his mind are silent, pinned to the shard of metal remaining in his head. He confesses to everything; he murdered Godwin and Hubert, he tried to kill the Doctor and Alfric, and he torched the Jewish house to make it appear that they were still blamed for Hubert's death. He insists that he was possessed by a demon which drove him to these acts, but he will be tried before the King's assizes, and his punishment meted out by the Franciscans. There will be scandal, but not as much as there could have been; and although the problems of the Jews are far from over, the stigma of murder has been lifted from them. The Doctor and Alfric attend Bacon, who burns his notes on the Elixir; he'd written about the Elixir in his youth, but now knows it was an impossible dream. The work he claimed to be doing was all nonsense, meant to humour Thomas. Bacon's notes on submersible craft and the movement of the planets have all been burned in the observatory, but now his notes on the Elixir have gone as well; he will go down in history as a teacher and philosopher, neither as the architect of a scientific revolution nor as a mad, heretical alchemist.

The Doctor returns to the castle to collect Nyssa, but is forced to tell her that her thesis is false. Bacon believes that the Universe is governed by the self-generation of likenesses, and he analyses the physical world only in the belief that understanding will protect the people of the world against the coming of the Antichrist. The science in his texts is almost incidental. Nyssa announces that she's decided to return home to her university, although well aware of the looming threat of war. It was not instinct but reason which led her to defend herself in the bower, for she now knows that the sanctuary she sought is an illusion. Life is a process of change and turmoil; true peace comes only with death, and she is not ready for that. She will accept responsibility for her own actions, and for Richard's death; but she won't allow that responsibility to crush her spirit. Satisfied, the Doctor takes her home, knowing that he too must take responsibility for his actions; now that he has met this older Nyssa, he will have to take extra care to keep the young Nyssa alive when she becomes his companion in the future.

This is the end of Thomas' quest. Accused of murder, punished by his order, and driven mad by the loss of the voices in his head, he ends his days as a vagrant walking the roads of England, seeking penance and sanctuary. Finally, in 1346, he is drawn to London by the fading memory of the voices. The ones he seeks are here, and a young man is about to go on a journey. Thomas tries to warn him of the futility of his quest, but the strangers, already taunted and abused by the angry townspeople, see only a mad priest haranguing them, and they brush him off and continue on their way without listening. The long wait has been for nothing; his warning goes undelivered. Events will proceed as they did before.