At the end of the tenth millennium, the elite of the galactic Union dine at the Crystal Bucephalus, a temporal projector which allows its patrons to dine at famous historical restaurants. The time equipment, designed by Alexhandri Lassiter, projects the visitors through Time with a reduced reality quotient, ensuring that they are able to spend brief periods in the past without altering history. And when Maximillian Arrestis, the kingpin of a criminal syndicate called the Elective, is poisoned by a bottle of wine sent from the Benefactor’s Cubiculo, the fact that it killed him proves that he was murdered by someone from his own time zone. The Maitre D’ retrieves and arrests the occupants of the Benefactor’s Cubiculo -- and the Doctor, Tegan and Turlough, who had just arrived at a quaint 18th-century French restaurant in the TARDIS, are surprised to be dragged over 8000 years into the future and accused of murder. Tegan impulsively flees into the corridors of the Bucephalus, where she meets Arrestis’ consort Diva -- who is being pursued by a man in a shielded combat suit. The man in the suit forces them both into an empty Cubiculo and transports them all into the past, intending to use Diva as bait to make his enemy show his hand.

The Doctor and Turlough appear to be in serious trouble until the Doctor realises where he is and reveals to the stunned Maitre D’ that he owns the restaurant. He had invested in the Bucephalus some time ago to dispose of the compound interest accumulating in his galactic bank account, and had never expected anything to come of the concept. Intending to find out who tried to frame him, the Doctor suggests that Turlough follow the Maitre D’ on his rounds to learn more about the galactic political situation, while the Doctor speaks with Lassiter about the technology used in the Bucephalus. Lassiter, happy to discuss his work with a fellow scientist, explains that his equipment generates time bubbles around his patrons, who are then navigated through the Vortex by a pool of Legions, multi-dimensional creatures recently released from a period of imprisonment imposed upon them by the Time Lords. The Doctor comes to suspect that Lassiter has deliberately retarded the full potential of his research in order to avoid creating an actual time machine, but before he can confront Lassiter on this, one of the Legions suffers a near-fatal infarction. Sven Tornqvist, the religious leader of the Lazarus Intent, has just invited the Maitre D’ to dine with him, but Turlough, fed up with the Maitre D’s supercilious and arrogant attitude, pushes past him into the Cubiculo… just as the injured Legion loses control of the time bubble, apparently exposing both Turlough and Tornqvist to the Time Winds.

Instead of disintegrating in the Vortex, Turlough and Tornqvist are transported to the Exemplar, the home of Lassiter’s former student and lover Ladygay Matisse. Through the Exemplar, she can control the functions of the Bucephalus without Lassiter’s knowledge, and she has used it to kidnap Tornqvist and find out what he knows about her ally. Tornqvist withstands the interrogation and is sent to the cells with Turlough to recover his strength before the next session. While recovering, he tells Turlough about his religion; founded over 5000 years ago, the Lazarus Intent has brought faith and comfort to most of the galaxy, and for all of that time its followers have been searching for a time machine with which to rescue Lazarus himself from his death at the hands of the Sontarans. Matisse’s son, Garrett Byson, arrives with food for the prisoners; due to his mother’s exposure to temporal radiation during her pregnancy, he has the body of a grown man although he is only nine years old. Tornqvist thus easily hypnotises the child with his Inf, the symbol of the Intent, and he and Turlough head back to the gateway, intending to force Matisse to return them to the Bucephalus.

The Doctor and Lassiter analyse the readings taken during the Legion’s attack, and discover that its infarction was deliberately induced by someone with technology equivalent to that of the Bucephalus. The Maitre D’, however, refuses to shut down the restaurant on their say-so, and since the Doctor is an absentee owner he is unable to insist. It occurs to the Doctor at this point to wonder why nobody from the Elective has responded to Arrestis’ murder, and when he examines the body he finds it to be a clone -- which should be impossible, since genetic research is forbidden by the Lazarus Intent and the technology to create a clone thus does not exist in this time period. Before he can convey his discovery to Lassiter, however, Matisse initiates the next stage of her plan and begins to alter the topography of the Carte de Locales…

The man in the suit has taken Tegan and Diva to 1980s London and allowed them to escape, but he soon tires of waiting and recaptures them, revealing himself to be the real Arrestis. He knows who Diva really is and why she agreed to become his consort, and thus tried to keep her running around in the past in order to force Lassiter to rescue her. Since it seems this is not going to happen, he contacts Matisse and orders her to return him to the Exemplar, but Turlough and Tornqvist break in and confront her before she can do so. Her android servants restrain them, but by the time she gets back to the controls, her earlier sabotage has taken effect, turning the Grid into a topographically closed system from which she cannot retrieve Arrestis. Unaware of the danger, Diva tries to use her own recall rod to return to the Bucephalus, but this simply transports her, Tegan and Arrestis to the next location on the Carte de Locales -- a private party on the planet Myrmidon, where gatecrashing is punishable by death. When Arrestis’ boorish behaviour draws unwanted attention, they are forced to flee to the next stop, but an anomaly in the Grid separates Tegan and Diva from Arrestis, sending them to the beautiful crystal world Diadem while Arrestis ends up in a bar on 20th-century Earth.

Lassiter calls in an off-duty Legion to help stabilise the Grid, but Matisse uses her connection to the Bucephalus to kill it. In its dying spasms, however, it alters the reality quotient of the active time bubbles, which means that Tegan, Diva and Arrestis become real enough to change the course of history. The remaining Legions are called in and the Doctor connects himself to the machinery as well to help sort out the mess, but when Matisse realises that a Time Lord has connected himself to the Grid, her greed for knowledge gets the better of her and she tries to scan his mind and learn his secrets. Trying to block her while simultaneously generating a new time bubble with which to recall Tegan and Diva, the Doctor is caught entirely off guard when the Legions -- still bitter about their imprisonment -- blast him into unconsciousness with the force of their thoughts. Matisse, disappointed, captures the time bubble which the Doctor had created and brings Tegan and Diva to the Exemplar, where Diva is revealed to be Hellenica Monroe -- Lassiter’s former colleague, and bitterly estranged wife.

Tegan and Monroe are locked up with Tornqvist and Turlough, and Monroe and Tornqvist explain the tangled personal situation to the Doctor’s companions. After Monroe left Lassiter, he and Matisse became lovers, and together, discovered that the crystalline alloy dichromide pentafluorate could be used to convert time spillage into harmless radiation. The centrepiece of the Crystal Bucephalus, the giant horse statue in the mezzanine, is in fact an integral part of the time projector. Lassiter, however, broke off all ties to Matisse when he learned that she was working for Arrestis and was trying to get close to him to gain access to his work. Monroe admits that she went undercover at Tornqvist’s request to reach the Crystal Bucephalus and find out if her suspicions about Lassiter were justified; she believes he has deliberately crippled his own work to prevent the Bucephalus from being used as a time machine which could fulfil the Lazarus Intent and bring their saviour back from the dead. But for some reason, Tegan gets the impression that Tornqvist would be just as happy if the Intent were never fulfilled.

Fearing that his reputation will be ruined if the Bucephalus doesn’t open on schedule, the Maitre D’ convinces Lassiter -- his brother -- to use his invention the Navigus to take over operation of the Grid until more Legions arrive to replace the two put out of action by Matisse. Lassiter reluctantly does so, still believing that Arrestis is dead and that he therefore has nothing to fear. Meanwhile, Arrestis kills a bouncer in a bar brawl, unaware that he is changing history by doing so. Matisse tries to retrieve him before the timelines experience embolism, but Lassiter detects her and locks her out. Fortunately, the Doctor recovers in time to work out why Matisse is showing her hand, and Lassiter thus lowers his defenses just long enough to let her retrieve her agent from the Grid -- still unaware that the man she is retrieving is Arrestis. As soon as he is sure that the course of history has been restored, Lassiter reactivates his defenses, shutting Matisse out for good -- or so he thinks. He then tries to send the Doctor back to 18th-century France to retrieve his TARDIS, but Matisse has another way into the Grid which Lassiter doesn’t know about, and she redirects the Doctor’s time bubble, leaving him stranded on the cold planet of Pella Satyrnis with no way of returning.

Monroe wires together her recall rod and Tornqvist’s, and uses them to emit a small EMP which disables Matisse’s androids. The prisoners then overpower Matisse and Arrestis while Monroe programmes the gateway to transport them back to the Bucephalus. Her control rod fails, however, and Tegan and Tornqvist are forced to flee back into the Exemplar while Turlough and Matisse flee into the gateway. Matisse sends her androids after Tegan and Tornqvist, shuts down the gateway, and releases a virus into the Bucephalus’ control systems. Soon after the restaurant opens, the time bubbles begin to degrade, threatening the lives of the patrons. Lassiter realises that he cannot correct the problem in time, and to prevent the deaths of thousands, he must retrieve his secret equipment from storage and turn the Bucephalus into a genuine time machine. By depositing its patrons fully in the past and then retrieving them, instead of leaving them half-in and half-out of the Vortex, he will protect them from exposure to the Time Winds. Matisse has successfully exposed the true extent of Lassiter’s work… and Arrestis therefore dismisses her from his service and sets off to the Bucephalus to collect Lassiter, the true genius. He leaves behind the shattered Matisse with nothing to show for giving up her chance at scientific immortality and betraying Lassiter, the man she had grown to love.

Instead of returning to the Bucephalus, Turlough and Monroe are transported to the 18th-century French restaurant where the Doctor and his companions had been dining when this all started for them. Having suddenly materialised out of thin air, they are accused of witchcraft by the terrified diners and are forced to flee for their lives. Kamelion lets them back into the TARDIS, and Turlough pilots the ship back to the Crystal Bucephalus. The temporal instability around the restaurant causes severe turbulence in the Time Vortex, but Turlough materialises safely; however, he still does not fully trust Kamelion, and orders him to remain in the TARDIS while he and Monroe contact the Doctor and Lassiter. Kamelion, certain that he can be of use, follows them out -- only to encounter Arrestis. He is immediately overwhelmed by Arrestis’ strong personality, and departs with his new master, forgetting to close the TARDIS door behind him.

Tegan and Tornqvist, searching for a way out of the Exemplar, instead find Arrestis’ quarters -- which are decorated with murals depicting the sadistic torture of alien life forms, with the vilest tortures reserved for the Sontarans. Tegan realises that Tornqvist is growing more distraught as they continue, as if something is shaking the very foundation of his faith, but he will not explain himself. Beyond Arrestis’ rooms they find a laboratory filled with cloned body parts, and a rare Inf similar to Tornqvist’s own -- confirmation of his worst fears. Matisse contacts them and reveals that she has allowed them to roam freely, in order to learn what Arrestis has been hiding from her -- but when Tornqvist shows her what he’s found, she realises the implications of his discovery as well as he does, and decides to cut her ties to Arrestis completely. Having detected the TARDIS’ approach, she sets off to steal it, shutting down her equipment behind her to prevent Tegan and Tornqvist from following, and intending to return for Garrett later in the stolen TARDIS.

Turlough and Monroe arrive in the Grid Control Room, and Monroe is furious to see that, just as she suspected, Lassiter developed true time travel but never told her, although he knew that her religion meant everything to her. Arrestis then arrives and demands that Lassiter hand over his secrets, and when Lassiter refuses, Arrestis has Kamelion shoot the Maitre D’ dead. Sickened, Lassiter finally reveals to Monroe that he developed a time machine years ago, and for love of her he used it to rescue Lazarus from the moment of his death -- only to find that “Lazarus” was Maximillian Arrestis, a megalomaniac criminal who founded an entire religious movement just to ensure his own immortality. Since his resurrection, Arrestis has established himself as the kingpin of the Elective and seeded the galaxy with clones of himself; thanks to the Intent, he is the only one in this time zone capable of creating such clones, and now, even if he is killed, his consciousness will immediately transfer itself to another waiting body. He is finally ready to reveal his true identity, take his position as the head of the Lazarus Intent, and become the ruler of the galaxy.

Stranded on Pella Satyrnis, the Doctor has only one choice -- befriend the natives and open a restaurant. After five years of hard work, the Tempus Fugit becomes the most famous restaurant in the world, and it is thus added to the Crystal Bucephalus’ Carte de Locales. As soon as the Doctor’s temporal monitors detect the presence of a servitor from the Bucephalus, he passes on ownership of the restaurant to his loyal apprentice and activates his recall rod… only to end up in the Exemplar instead. There, he is reunited with Tegan and Tornqvist, and discovers that in her haste Matisse made an error while shutting down her equipment, causing the power to feed back to its source -- a singularity which will wipe out this entire solar system if it explodes. Unable to contain the damage, the Doctor decides to close off the power grid and transport it into the Vortex, where it will explode out of harm’s way. However, Garrett presses the wrong button at the wrong time, trapping himself, the Doctor, Tornqvist and Tegan in the control room when it dematerialises…

Matisse arrives in the Bucephalus and locates the TARDIS, but presses the wrong controls and accidentally dematerialises. The turbulence generated by the link between the Bucephalus and the Exemplar causes the TARDIS to stall in the Vortex, and when Matisse tries to use the telepathic circuits to find out how to put things right, the sheer amount of information flooding through them knocks her out. Meanwhile, the Doctor opens a gateway to the Bucephalus, and urges the others through ahead -- but the gateway intersects the path of the TARDIS, and they end up there instead. There is still no sign of the Doctor when the Exemplar explodes, releasing a shock wave of indescribable power -- and the TARDIS, caught in the wave front of the Vortex rupture, begins to absorb more energy than it can safely contain…

As a loyal follower of the Lazarus Intent, Monroe seems to have no choice but to pledge obedience to Arrestis. She therefore offers to use the Bucephalus to open a time gate to Hexdane, the capital of the Lazarus Intent, but is unable to do so due to the turbulence of the Vortex rupture. The buffers in the Bucephalus are flooded with more time spillage than they can handle, and Arrestis therefore takes Monroe and Turlough back to his ship, leaving Kamelion to guard Lassiter while the scientist ensures that the time buffers do not overload. Once Arrestis has gone, however, Kamelion submits to Lassiter’s will, and Lassiter orders him to kill Arrestis. The Doctor, meanwhile, survives his trip through the Vortex and arrives back in the Bucephalus, where he and Lassiter discover that the situation is worse than they’d thought. The TARDIS is absorbing most of the energy released by the Vortex rupture, and when it reaches its capacity, it will explode -- flooding the Bucephalus’ buffers with a massive blast of time spillage, and causing a chain reaction which could wipe out most of the inhabited galaxy.

As the TARDIS begins to disintegrate, the childlike Garrett hears it speaking to him and guides the others to a place of safety. Their route takes them through the library, where Matisse lags behind collecting the books which will reveal the secrets of the Time Lords -- and is swept away into the Vortex when the library disintegrates around her. Garrett guides the others to a platform overlooking a set of interconnected domes and pillars -- a representation of the TARDIS itself, which is blowing to bits as they watch. Knowing that he will soon be dead, Tornqvist confesses to Tegan that he has suspected for some time that Arrestis was Lazarus -- suspicions which were confirmed in the Exemplar when he found Lazarus’ personal Inf in Arrestis’ quarters. He now believes that Arrestis had him kidnapped to find out how close he was to the truth. His faith has been shaken by the shock of learning the truth about his saviour, but Tegan reminds him that, whatever the reasons for its creation; the Lazarus Intent has brought hope to the galaxy; the faith is stronger than its founder.

Arrestis survives Kamelion’s attack and returns to Grid Control to collect Lassiter, but once there Kamelion again submits to the Doctor’s will. The Doctor sends Kamelion to destroy the Bucephalus statue, hoping that the sudden release of energy from the time buffers will jar the TARDIS out of place and cause it to materialise. As soon as Kamelion has gone, Arrestis orders the Doctor to add his expertise to Monroe’s and generate a stable time gate to Hexdane. The Doctor reluctantly does so, but as soon as Arrestis has gone, Monroe admits that she knows the difference between the faith and its founder, and that she changed the gate’s co-ordinates. Meanwhile, Kamelion destroys the statue, and as the Doctor had hoped, the TARDIS is blasted free of the Vortex and materialises in the mezzanine. As the energy from the Vortex rupture floods into the Bucephalus’ time buffers, the Doctor uses the restaurant’s temporal projector to send it back in Time with a reduced reality quotient, ensuring that it dissipates harmlessly.

Lassiter and Monroe are reconciled, and Lassiter finally meets Garrett, his son. Tornqvist, his faith restored, promises to ensure that the Lazarus Intent will carry on helping the people of the galaxy through the dark ages which the Doctor tells him are to come. Kamelion, realising that he cannot be trusted, decides to remain in the TARDIS from now on while the Doctor and his companions venture outside. The Doctor decides to take his companions to the Eye of Orion to relax while the TARDIS repairs itself. And elsewhere in time and space, Arrestis emerges from the time gate, expecting to find himself on Hexdane -- only to realise, too late, that Monroe has sent him back in time to Sontar at the exact moment of his death…