The TARDIS materialises in the Uva Beta Uva planetary system on the Rock of Judgement, an asteroid prison fortress where the system’s criminals are tried and sentenced. Frank Spiggot, a maverick cop who plays by his own rules, has just inflicted himself upon High Archon Pyerpoint and is demanding access to the Rock’s security system in order to investigate reports of anomalies in the computer net. Pyerpoint refuses to circumvent the rules to allow him access, but soon after he kicks Spiggot out of his office, the Doctor and Romana are arrested for trespassing, and while Pyerpoint is questioning them Spiggot hacks into the computer net. He too is arrested, but before Pyerpoint can take action he receives a call from Planet Five ordering him to allow Spiggot to carry out his investigation. Pyerpoint assumes that the Doctor and Romana are also agents from Planet Five, sent to distract him while Spiggot goes about his business, and Spiggot, who believes them to be harmless travellers, plays along with the error in order to keep Pyerpoint off guard. The Doctor’s curiosity is piqued by Spiggot’s behaviour, and he decides to help Spiggot in order to find out what’s really going on.

Margo, the Rock’s chief of security, has been hearing voices in her head for the past month, and has begun to scribble calculations and co-ordinates without knowing what they mean. She also begins sleepwalking, first to artist Menlove Stokes’ gallery and then to the observation deck, where the Doctor and Romana see her suffer a total nervous breakdown when she finds herself looking for something without knowing what it is. Pyerpoint, apparently concerned for her well-being, has her confined to her quarters and orders her deputy Shom not to report her condition to anyone. The Doctor and Romana, meanwhile, visit the art gallery, where Stokes displays artwork inspired by the most notorious criminals ever brought to the Rock, including a helicon death-mask of the psi-killer Xais. They slip out during an angry confrontation between Stokes and his intern Zy, who has put in a bid to buy the gallery once Stokes’ lease runs out. Zy storms out, leaving Stokes alone in the gallery -- where an unseen assailant knocks him out. He assumes that his attacker was Zy, but in fact it was Margo, who has trashed the gallery to cover her theft of Xais’ death-mask. Once wearing the mask, she becomes possessed by an insatiable hatred of Normals, and indulges her rage by locating an innocent passer-by and telekinetically crushing him to death. Since her chosen victim was Zy, Pyerpoint has Stokes arrested for the murder.

The Doctor deduceds that Spiggot is not telling them the whole truth and confronts the detective, who admits that his claim about the computer system, while true, is just a cover for his real mission. An expedition seeking precious minerals on Planet Eleven was recently slaughtered when someone psionically crushed the base’s environment engineer to death and sabotaged the life support system. Xais, who blamed “Normals” for the extermination of her people, was the only killer ever known to crush her victims with the power of her mind… but she was executed on the Rock three years ago. The Doctor has K9 check out the Rock’s computer net, and K9 confirms that it has been infiltrated; someone secretly transmatted themselves to Planet Eleven at the time of the murders, and is currently sending an undetectable transmission into space. Margo then sabotages the computer net, bringing down the Rock’s defences and damaging K9, and then flees into the corridors of the Rock. Shom pursues her, but she kills him. As Romana attempts to repair K9, the Rock is attacked; the calculations which Margo was scribbling enabled Xais, who is now entirely in control of Margo’s body, to work out the location of the Rock and transmit a homing signal to her allies. Pyerpoint orders the evacuation of the Rock while he remains behind to face the intruders.

The Doctor sends Romana back to the TARDIS while he and Spiggot confront the intruders. Xais is waiting by the airlock, and although the Doctor tries to help Margo resist Xais’ control, he fails and is captured by her allies -- the criminal Nisbett brothers Charlie and Eddie, and their Ogron thugs. Spiggot flees, pursued by the Ogrons, while Xais, believing the Doctor to be a security agent from Planet Five, holds him for interrogation to find out how much the security forces know about her. She also has Pyerpoint taken prisoner, claiming that she wishes his punishment to be long and painful; the Nisbetts, who have fallen on hard times since their establishment contact Sentinel betrayed them, have no choice but to play along for the time being. Xais claims to need their help to mine out the resources of belzite on Planet Eleven; in return she will give them a cut of the proceeds and reveal the true identity of Sentinel. Charlie, however, believes that she is using them for some other purpose, and intends to play along until he finds out what she is really after, then kill her and take it himself.

The Nisbetts send the Ogrons to clear the Rock of any other occupants, but most of its staff and prisoners have already evacuated. Romana manages to evade the pursuing Ogrons, but their wild shots after her bring down the roof around the TARDIS. She is reunited with Spiggot and with Stokes, who got lost and was unable to reach the escape pods in time. Leaving K9 and Spiggot to clear the rubble from around the TARDIS, she sets off to rescue the Doctor, and Stokes, who prefers her company to that of Spiggot, follows her. They manage to convince the Ogron guard on the airlock that they are friends of the Nisbetts, and enter the ship only to find that Xais has already taken the Doctor away for torture. Nevertheless, they rescue Pyerpoint, who seems to take the invasion of the Rock as a personal insult. He takes them to his office, claiming that he must send out a personal distress signal -- but once there he locks them inside and releases poisonous gas into the room…

Xais places the Doctor in the particle reversal chamber and prepares to torture him, but Margo resurfaces just long enough to release him. With access to Xais’ memories, Margo now knows that for years now, Pyerpoint has been using insider information and criminal contacts to amass a fortune and wield power as the anonymous kingpin of a criminal empire. He and Xais were allies when she was free; he directed her towards his enemies, allowing her to indulge her hatred of Normals while eliminating all threats to his own empire. Xais learned that her powers enabled her to record her own brain patterns in liquid helicon; she was captured before she could put this discovery to use, but thanks to Menlove Stokes, she was able to survive her own death by imprinting her mind in the helicon mask. It has taken her three years to regain her strength and seize control of Margo’s mind, but now, with the unwitting help of the Nisbett brothers, Xais intends to mine the helicon out of Planet Eleven, having used Margo to dispose of the survey team which could have summoned a corporation to her territory. She has promised Pyerpoint that she will copy his mind into the helicon as well, granting him immortality, but in fact she intends to create an army of helicon duplicates and destroy all Normals. The Doctor flees as Xais’ mind reasserts itself, wiping out Margo’s identity for good.

K9 successfully clears the debris away from around the TARDIS, but Spiggot, unwilling to stand around doing nothing, decides to sabotage the Rock’s engines to prevent Xais and the Nisbetts from reaching their destination. K9 agrees to help, but makes an error and sends the Rock spiralling towards the surface of Planet Eleven. Meanwhile, the Doctor rescues Romana and Stokes from Pyerpoint’s office and explains the situation to them, but when the Rock goes out of control they must go to its control room to correct the malfunction, although this means that they are recaptured by Xais and the Nisbetts. Charlie decides to let them live, since the Doctor has proven he can be useful. Xais, the Nisbetts and their prisoners transmat to the doomed survey team’s base on Planet Eleven, while the Ogrons follow in the Nisbetts’ ship. K9 and Spiggot attempt to follow in the TARDIS, but when K9 programmes it to detect any artificial power sources on the planet’s surfaces, he finds a second base in the mountains. He and Spiggot investigate, to find that someone has set up an automated mining unit which has been functioning at full capacity for months…

The Nisbetts’ prisoners are locked in a store room while Charlie sends out an automated probe to analyse the planet’s mineral content. The Doctor and Romana use some of the stored explosives to blast open the door and escape, but the terrified Stokes has had enough and takes his leave of them, seeking somewhere to hide. The Doctor and Romana reach the base’s control room just as the probe returns, with data that indicates that the planet’s helicon content is now negligible. Xais is enraged, and the Doctor takes the opportunity to reveal to the Nisbetts that Xais planned to mine not belzite but helicon, which is useless to anyone but her. Eddie tries to pull a gun on Xais, but she crushes him to death, and the furious Charlie shoots her in the chest repeatedly, killing Margo’s body. Pyerpoint flees into the depths of the base with Xais’ mask, and when Romana pursues him, he forces the mask onto her face. Charlie, meanwhile, ties the Doctor to a chair and reveals that he has rigged the base with explosives as a precaution in case Xais betrayed him. Once he and the Ogrons are clear, he will detonate them, and the explosion of the base’s fusion reactor will take out a large part of the planet as well.

Pyerpoint takes the unconscious Romana to his secret mining base, unaware that Stokes is hiding aboard his shuttle. When Xais awakens in Romana’s body, she finds that Pyerpoint has pinned her down in a force field which restrains her powers; he has already mined out all of the helicon from the planet, and he now threatens to kill Xais unless she provides him with the formula with which to transfer his mind into the helicon. Meanwhile, Stokes is reunited with Spiggot and K9, and when he tells them that the code word which Pyerpoint used to unseal the airlock was “Sentinel”, Spiggot realises that Pyerpoint was the establishment contact who betrayed the Nisbett firm. He tries to contact Charlie and use the information to bargain with him, but this news only makes Charlie even more determined to destroy the planet, thus taking out Xais and Pyerpoint in one blow. Pyerpoint, having monitored the call from his base, realises that he has no choice but to release Xais to help him escape -- but his usefulness is now over, and she releases a psionic blast which nearly kills him. She has already dealt with the possibility of betrayal by the Nisbetts, and as the Ogrons prepare to leap into hyperspace to avoid the shockwave from the exploding planet, they trigger a booby-trap in the navigational system which causes the ship to tear itself apart before Charlie can send the detonating signal.

The Doctor frees himself and recircuits the transmat to send him to Pyerpoint’s base. Xais has primed the helicon, and is preparing to imprint it -- but at the last moment, Romana, who has been gathering her strength, regains control of herself and flings the mask away. The dying Pyerpoint finally realises that Xais lied to him, and had no intention of transferring his mind into her helicon. Enraged, he activates one of the base’s guardian robots and orders it to destroy all intruders, but Xais, seeking a new host, manages to convince him that it is indeed possible for her to transfer his mind into the helicon if he wears the mask. Desperate for immortality, he does so, but as he and Xais struggle for control of his body, the guardian robot finds and kills him. Xais is thus left without a host, and is unable to focus upon the primed liquid helicon. The Doctor, Romana, K9, Spiggot and Stokes flee in the TARDIS as the helicon surges out of control, covering and consuming the surface of the planet. Xais’ mind is still imprinted in the helicon, but she cannot control it and will thus remain trapped on Planet Eleven forever. The Doctor returns Spiggot and Stokes to the Rock of Judgement, and gives Spiggot a chemical formula with which the system authorities can render the helicon harmless, destroying Xais forever.