As the TARDIS travels through the Vortex, the Doctor and Polly both experience a dream or vision of a young Goth man calling to them for help while being attacked by a humanoid figure with the head of a cat. The TARDIS then materialises in 1994, near an old Victorian mansion called the Grange. A team of students has just arrived on a ghost-hunting expedition, and the bursar Miss Thorsuun and her acerbic assistant Kerbe have insisted that the house be sealed off from the outside world for the duration of their experiments; however, the Doctor bluffs his way in by claiming to be an associate of Professor Bridgeman’s, and Bridgeman, already unnerved by Thorsuun and Kerbe’s intensity, plays along with him in order to get an ally. While setting up his equipment, one of the students is startled by the spectre of a screaming Victorian woman, and falls downstairs, breaking his arm. Bridgeman defies Thorsuun and leaves the house to call an ambulance, but as he nears the village phone box he sees the ghost of the Victorian woman pushing a giggling, senile old man in a wheelchair -- and before he can call the hospital, he vanishes in a burst of light.
Ben and Polly, amazed by the remarkable technology which the students are using, leave the Grange to explore the nearby town, but suffer from culture shock when they see just how much the world has changed in the past 28 years. Meanwhile, Thorsuun confronts the Doctor, having realised that he and his friends are time travellers; but before she can explain why she needs his help, her other allies arrive. In her desperation to escape from the Earth, Thorsuun has contacted the Cat People, feline predators who are searching for a new energy source for their dying homeworld. The Cat People’s leader, Queen Aysha, is aware that the litter-runt Lotuss intends to stage a coup and overthrow her, but she has allowed Lotuss’ ambitions free rein, intending to channel her anger and frustration towards the primitives of Earth. If Thorsuun betrays them, or her plans come to nothing, the Cat People can always exterminate all life on Earth and strip the planet of its resources.
The young man from the Doctor and Polly’s visions, Atimkos, is also on his way to the Grange, and he won’t let anybody get in his way. When a homeless girl accosts him at the train station, demanding change, Atimkos sings a harmonic which dissolves the flesh from her outstretched arm and disintegrates her dog. Realising that he has overreacted and is attracting unwanted attention, he then sings time to a stop and heads for the Grange in the stillness. He had been trying to contact the Doctor telepathically earlier, but he now believes that Polly is more suitable for his purposes...
While studying the Grange’s library, the Doctor finds a book coated in reverse tachyon-chronons -- a disguised RTC unit over which time flows backwards. He uses it to heal Peter’s broken arm, and as he’s holding the RTC unit he is unaffected when Atimkos stops the flow of Time. But Thorsuun has an RTC of her own, which has prevented her from aging over the millennia, and which she uses to protect herself and the Cat People. The Cat People kill Kerbe, but before they can kill the students the Doctor flings his RTC into the room where they’re hiding. This is the room where they’d set up the ghost-hunting equipment, which has nullified all exterior sound; when the RTC is placed within this Ex-Area, it becomes a temporal null zone which the Cat People cannot penetrate. The angry Cat People take Thorsuun and the Doctor back to their shuttle, where Thorsuun explains that she is a Euterpian, one of a race of songsmiths who once travelled the Universe in ships piloted by sound waves. Forty thousand years ago, five Euterpians arrived on Earth to plant a line of beacons which, once illuminated, would give their mothership a line along which to cut open the planet and convert it into a new fuel source. Before they could begin, however, the mothership was destroyed by a random solar flare, and the members of the spearhead have been trapped on Earth ever since. Thorsuun has finally succeeded in contacting a species with the resources to activate the beacons, and she arranged to meet them here in the belief that the Victorian “ghosts” were in fact two other Euterpians who had been trying to contact her; if she’s correct, then there must be a beacon buried nearby. But now that the Cat People have arrived, Thorsuun is beginning to realise that they’re not the most reliable of allies.
Atimkos arrives at the Grange, where he meets Ben and Polly and tells them that he’s come to stop Thorsuun from destroying the Earth. While Ben tries to contact the Doctor and warn him of the danger, Atimkos and Polly return to the Grange, where Atimkos uses his own RTC unit -- disguised as a pack of Tarot cards -- to penetrate the Ex-Area and contact the students. Using his RTC unit and the book in conjunction, he travels back to Victorian times and contacts the “ghosts”, Dent and Wilding -- or rather, Udentkista and Tarwildbaning, two more Euterpians. Wilding explains that their team leader, Godwanna, had retreated from Earth to a garden she created in a hyperspace nexus point, and there she had begun to experiment upon kidnapped humans in order to release their psychic potential and use them to activate the beacons. When Dent and Wilding protested against her cruelty, Godwanna expelled them from the garden, and inflicted upon Dent brain damage which Wilding has been unable to heal. Godwanna sealed off the nexus point behind them and continued her expeirments; Bridgeman and a young Australian hiker named Nate Simms are only her latest victims. The Euterpians compare notes with the students, and realise that they’ve been on Earth for so long that they failed to notice the gradual process of continental drift -- and that the straight line they laid millennia ago has since broken up into a pattern. Polly realises that the lines of force which they’re describing are ley lines, and Atimkos realises that the Grange must lie on one of those lines; and if Thorsuun realises this, she can use it to locate and activate the nearest beacon before Atimkos is ready for her.
Ben is captured by the Cat People, but the Doctor convinces Aysha to let him live as a hostage to ensure the Doctor’s own good behaviour. Ben tells Aysha of Atimkos’ arrival, and Aysha sends Jayde to the Grange to investigate -- but on the way Jayde unexpectedly encounters another Thorsuun, who claims to have returned to the Grange to prevent her earlier self from making a grave mistake. Jayde doesn’t understand Thorsuun’s attempts to explain how she can be in two places at once, and thus kills her and continues on to the Grange. There, Atimkos and the students have just returned, and when Jayde attacks, Atimkos uses his RTC unit to regress her to the age of a kitten; but then, in order to stop Thorsuun from activating the beacons, he destroys the students’ ghost-hunting equipment. Just to make sure that Thorsuun has been stopped, he drags Polly out of the house before she can protest and sings the ley line active -- releasing a fraction of its power to blow up the Grange, with the students still trapped inside.
Refusing to accept failure, the younger Thorsuun sings the Cat People’s shuttle into the ley line and uses her RTC to transport it along the line to another beacon. The shuttle materialises in ancient Baghdad, where the Doctor and Ben manage to trick their guards and escape into the city with the help of a young pickpocket, Aroon. Aroon believes that the Cat People are sand demons here to destroy his city, and he’s not too far off; Thorsuun intends to activate the nearby beacon and use it to locate the others, knowing full well that the subsequent energy release will destroy Baghdad. The Doctor therefore disguises himself as a blind crone, steals the power pack from Lotuss’ gun, and has Aroon plant it in Thorsuun’s cloak, to make it appear as though Thorsuun has betrayed her allies. Thorsuun is forced to flee from the angry Cat People, and after sending Aroon to safety the Doctor helps her to escape; she is thus forced to help him and Ben try to steal the Cat People’s shuttle so they can return to 1994. However, the Cat People are waiting for them, having analysed the harmonics of Thorsuun’s song and programmed their shuttle to reproduce them. They no longer require Thorsuun’s services, and thus they abandon her in Baghdad and take the Doctor and Ben back to 1994 to collect the TARDIS, intending to force the Doctor to take them back in time and activate the beacons at the height of their power. Thorsuun, furious, vows to return to the Grange when 1994 rolls around again, to stop her earlier self from making the grave mistake of trusting the Cat People and the Doctor...
Realising that Atimkos has betrayed them, Dent and Wilding return to the nexus point where Godwanna abandoned Bridgeman and Simms, having destroyed their minds with her failed experiments. To save themselves and the Earth, Dent and Wilding must find Godwanna’s garden before Atimkos activates the beacons; Wilding therefore attempts to communicate with Simms and Bridgeman and heal the damage to their minds, despite the risk that she may make matters worse. She is unable to save Simms, but Bridgeman recovers, not only regaining his sanity but overcoming the buried fears and guilt over his parents’ deaths which have weakened him all his life. Now brimming with self-confidence, he sees what Dent and Wilding were never able to perceive; this nexus point is itself the garden, and Wilding really did manage to cure Dent’s brain damage. Godwanna did not cut them off from the garden; she simply blocked the truth of it from their minds.
Atimkos sings Polly into a daze, hypnotising her and blocking her memory of what happened to the students. She accompanies him to London to buy a plane ticket to Australia, where the Euterpians first landed on Earth and where he believes the nexus point to Godwanna’s garden is located. Polly remains under his control until they reach Australia, where he allows her memory to return and reveals that he’s been using her for his own ends; she is a naturally gifted psychic, and he can use her gifts to activate the beacons. Even though she knows she’s playing into his hands, she cannot control her rage, and Atimkos taps into her outpouring of emotion and uses it to activate the beacons -- and destroy the Earth.
The Doctor slips away from his guards on the Cat People’s ship, and finds a bomb which Lotuss has set to destroy Aysha’s shuttle upon its departure. He warns Aysha of the danger, and she tricks Lotuss into accompanying her to the shuttle bay, where she triggers a decompression alarm. Lotuss instinctively takes shelter in the shuttle, and Aysha launches it into space, causing Lotuss to be killed by her own trap. Satisfied, Aysha orders the Doctor and Ben to pilot her to Godwanna’s garden in the TARDIS, using Thorsuun’s RTC to override the faulty TARDIS navigational system. Atimkos and Polly have already arrived, bearing the energy sphere which contains the compressed essence of the planet Earth. Atimkos reveals that he was working for Godwanna all along; now, by releasing the energy contained within the sphere, the Euterpians can return home. However, the Doctor informs the Euterpians that their civilisation is long extinct; they have no home to return to. Godwanna refuses to believe him, but before she can sing the globe into extinction, the deranged Simms recognises her as the woman who hurt him so badly, and attacks her. Atimkos kills Simms with his RTC, and “accidentally” kills Godwanna as well. Now intends to control the energy globe -- but Dent and Wilding reveal that they prefer their lives on Earth to the company of their fellow Euterpians, and they give the globe to the Doctor. Atimkos chases him into the TARDIS to retrieve it, but the Doctor removes his ship’s Time Vector Generator and flees, trapping Atimkos in a hollow police box shell. Atimkos tries to sing his way out, but the indestructible interior of the police box reflects the sound back, and he disintegrates himself.
Aysha takes Polly hostage and demands that the Doctor hand over the globe, but he gives Ben a cricket ball before doing so, and Ben uses it to knock the globe out of Aysha’s hands and into Dent’s. Realising that she is now outmatched, Aysha uses Thorsuun’s RTC unit to return to her ship -- but her crew interpret the unfamiliar approaching energy signature as an attack and open fire, killing Aysha and creating an energy lash-back which destroys their ship. The Doctor, Polly, Ben and Bridgeman return to the TARDIS, and Dent and Wilding sing it back to the Grange moments before the explosion so the Doctor can rescue Bridgeman’s students. Dent and Wilding, the only Euterpian survivors, will remain on the Earth, where they have come to feel at home.