Sarah Jane visits Betterworth's Supermarket to shop for groceries. Luke usually does the shopping for her, and for a local pensioner named Ploughman, as he appreciates the mental puzzle of calculating the totals and working out the most efficient route around the aisles; however, he's currently doing work experience at the Natural History Museum, and in any case, Sarah Jane hasn't seen Ploughman since he started complaining about the construction works behind his house a few weeks ago. When she arrives at the supermarket, she is amused to find that Clyde is doing his work experience here, under the self-important young manager, Charlson. Charlson is expecting a visit from the regional manager, and when Sarah Jane finds him berating Clyde for allegedly piling up cans in an unhelpfully artistic fashion, she intervenes, praising Clyde's helpfulness and drawing him away from the still irritated manager. Once they're free, Clyde tells Sarah Jane that he's been trailing an old man who has been acting oddly. Sarah Jane recently repaired Clyde's broken watch with her sonic lipstick, and when the old man walked past him, the hands of the watch started to spin uncontrollably. Sarah Jane's sonic lipstick then begins to buzz and rattle inside her purse, just as the old man in question walks past. He is wearing thick spectacles and operating what appears to be a pocket calculator, and Sarah Jane recognises him as her missing neighbour, Mr Ploughman.
Ploughman notices Sarah Jane and Clyde watching him and tries to give them the slip, but in his haste, he bumps into a woman and drops his spectacles. Clyde follows Ploughman as Sarah Jane apologises for her "uncle," and the woman, somewhat mollified, hands over the spectacles, which had fallen into her trolley. Sarah Jane notices that their lenses are oddly iridescent, but before she can examine them more closely, she hears Clyde cry out. Somehow, cages full of milk cartons have rolled out to block his way through the dairy section, and the adjacent aisle has been walled off by stacks of cans, which fit into place so suddenly that several customers and a free-sample lady have been trapped between them. Sarah Jane and Clyde detour through the cereal aisle, but Ploughman waves the device he's carrying at them, and loaves of bread fly off the shelves, piling themselves into a barrier. Clyde pushes his way through the wall of bread and catches Ploughman in the frozen-foods section, but the aged Ploughman leaps nimbly up onto a freezer cabinet, and food begins shooting out of it as if from a cannon. Clyde lunges forward to grab Ploughman, who drops his "calculator" and falls to the floor; however, Clyde also overbalances and falls into the freezer. Sarah Jane runs up to help him out, but sees that Clyde appears to have fallen into a frozen pit that extends much further than the bottom of the freezer.
Charlson arrives on the scene and orders the store's security guards to throw Ploughman out, and when Sarah Jane turns to look again, she sees that the freezer has returned to normal -- but Clyde is holding a large cube with alien writing on the side, and seems oddly subdued. When Charlson starts to berate him for making a scene, Clyde raises his hand, and a flash of light blasts Charlson across the aisle, knocking him senseless. Clyde walks out of the store, and when Sarah Jane tries to follow him, cereal explodes out of the boxes on the shelves and coalesces into a humanoid figure. Sarah Jane instinctively raises her arm to defend herself -- and since she's holding Ploughman's spectacles in that hand, she sees ghostly tendrils of light through its lenses, operating the cereal monster like a puppet. More monsters made out of raw deli meat, tin cans, toilet paper, and melted chocolate hold Sarah Jane back until Clyde steps out of the store, at which point the monsters collapse into raw groceries.
Before Sarah Jane can follow Clyde, she receives a phone call telling her that Luke is in trouble. She immediately rushes to the museum, and to her surprise, she catches sight of Ploughman entering the building when she arrives. When she holds his spectacles to her eyes, she sees more tendrils of light snaking about the display cases. Luke's supervisor, Dr Minot, then arrives and tells Sarah Jane that Luke has stolen a valuable exhibit and locked himself in a storage closet. Sarah Jane shoos away the security guards clustered around the closet and uses her sonic lipstick to open it; once inside, however, she seals it behind her, to give herself a chance to speak to Luke alone. Luke is huddled on the floor, holding the valuable 82-carat Black Diamond of Ernfield, a cursed jewel said to have been stolen from a mid-14th-century temple. He calmly tells Sarah Jane that most black diamonds contain iron oxide, magnetite and hematite, but this one felt different to him somehow. Sarah Jane's sonic lipstick begins to buzz again, and she sees that the hands of Luke's watch are spinning -- and when she takes a close look at the diamond, she realises that the striations resemble the alien writing that she saw on the cube Clyde took out of the supermarket.
After Luke's brief moment of lucidity, his expression goes slack and calm, just like Clyde's. People have started hammering on the door of the closet, and Sarah Jane opens it and guides Luke out -- only to find that the guards weren't knocking to get in as she thought. Ploughman is standing outside, operating his calculator device, and the security guards have been rendered unconscious. Luke makes a break for it, holding up the black diamond as he runs, and through the spectacles, Sarah Jane sees tendrils of energy lashing out around the exhibits and animating them just like the goods at the supermarket. Egyptian animal mummies and dead butterflies come to life and hold Ploughman back while Luke escapes, and when the guards in the entrance hall try to intervene, the diplodocus skeleton explodes into bits and reassembles itself around them, trapping them in the ribcage. The turmoil delays Sarah Jane long enough for Luke to disappear into the crowds outside.
Sarah Jane rushes back to Bannerman Road to consult Mr Smith, but Gita Chandra, who has returned home for lunch, stops her on the way to gossip about the strange gust of wind that blasted through her house a moment ago. Rani steers her mother away, claiming that she's doing her work experience with Sarah Jane, and tells Sarah Jane that she saw Mr Ploughman snooping around earlier; Rani tried to speak to him, assuming that he was looking for Luke, but he waved his pocket calculator device at her and an odd gust of wind blew through her house, causing the flowers in her living room to bunch together into a menacing face. The wind then blew the door shut, and the face collapsed back into flowers.
Sarah Jane and Rani consult Mr Smith, who identifies the "spectral specs" as construction tools from the planet Persopolis; they enable construction workers to see the otherwise invisible force fields they use to manipulate their tools and raw materials. Mr Smith examines his historical database and reports that a Persopolesian craft may have collided with Halley's Comet in 1066 and crashed to Earth. The ship's failsafe would have broken the control console into three separate components to prevent the advanced technology from falling into primitive hands, but each segment is programmed to influence any innocent minds in the vicinity to keep it safe. Presumably, the black diamond and the cube are forcing Luke and Clyde to protect them from Mr Ploughman. Rani then looks out of the window while wearing the specs, and sees a trail leading down the street -- presumably the trail of energy that Ploughman left as he walked away. She and Sarah Jane follow the trail in Sarah Jane's car, and see two more trails of energy, presumably Clyde and Luke, converging on the third. The trails lead to an old scrapyard, and Sarah Jane overtakes the others, gets there first, and uses her wrist scanner to locate the final component in a precariously balanced old Ford Zephyr. Rani climbs up to fetch it, but falls under its influence the moment she touches it.
Ploughman then arrives with Clyde and Luke trailing behind him, and reveals that the pensioner's body is now possessed by the Persopolesian pilot, Janxia. He has been in suspended animation for 1000 years, and was woken when Ploughman trespassed in the construction site behind his house and stumbled upon Janxia's escape pod. It's taken him some time to regain his strength, and he was initially unable to control the control segments when he found them, which is why they used Clyde and Luke to defend themselves from him; however, he has now reasserted his control over them and intends to return home, even though most of southern England will be destroyed when he launches his ship. Sarah Jane offers to put him into contact with people who can move his ship to an unpopulated area before the launch, but Janxia doesn't care what collateral damage he inflicts in his escape from Earth.
Sarah Jane activates her sonic lipstick, reasoning that it will interfere with the Persopolesian artefacts just as they interfered with it. Janxia angrily turns the full power of his control unit on Sarah, freezing her in place, but he's still not strong enough to control everyone at once, and the children break free of him. Angered, Janxia separates his essence from Ploughman, who faints upon seeing the alien standing next to him. Janxia then uses the control unit to generate more force fields and create monsters out of the junked cars, but Luke, Clyde, and Rani create more monsters to fight his using the control components. While Janxia is distracted, Rani and Luke toss the diamond into the scrapyard's car crusher, and Clyde activates its controls. The desperate Janxia rushes forward to retrieve the diamond, but slips on the poorly balanced Zephyr and falls into the crusher just as its jaws shut.
Sarah Jane assures her stricken friends that there was nothing they could have done to save the obsessed Janxia. They take Ploughman back home, and when he wakes, they tell him that he's had a bad dream. Clyde is now barred from Betterworth's for life, but doesn't much care. Sarah Jane has Mr Smith create a new black diamond for the museum, and convinces Dr Minot not to press charges against Luke by donating another alien jewel from her private collection. As a replacement souvenir, she keeps the Persopolesian control cube, which Janxia dropped before he fell into the crusher.