A foreign airliner crashes in England and workers gather the unclaimed luggage and put it into storage. Two airport officers sort the luggage and then start to leave, but the light flicker. The younger officer moves a case over so he can get up on the table and check the light, and the light goes out entirely. When he climbs down and moves the case away, the light goes back on. The officers realize that there's something in the case and open it, and find a typewriter inside. The younger officer points out that his radium watch is glowing.
The airport supervisor calls Peter and Sir Charles, who get the case and open it inside of a lead-shielded compartment. As the minister arrives, Peter gets the open case and they tell the Minister that the case contains an atomic core of uranium-235. Peter explains that it's used in the manufacture of an atomic bomb, and that someone is smuggling them into London and other world capitals to set and detonate them with a radio signal. Anyone could assemble a bomb from parts found in England, except for the atomic cores. Two half cores are required to set off the bomb, and Peter figures that the other atomic core is already in England. There are no clues on the passenger list indicating who had the case and there's no other indication of where to start. Peter figures that whoever is responsible is already bringing in a replacement core.
Lady Helen Peversham, woman's golf champion, finishes a match in Scotland and goes to her hotel room to pack for her return to England. Her chauffeur Hanstra comes in and tells Helen about the travel arrangements. When Helen wonders where her golf bag is, Hanstra claims that he sent them out to be cleaned. Their ferry is ready to live, and a messenger returns with the golf bag. At the customs desk, the officer inspects their luggage and checks a hidden Geiger counter. He notices that it's reacting to Helen's golf bag but lets her pass through. He then calls Whitehouse and Sir Charles soon informs Peter. Both men are surprised to hear that Helen has the atomic core since both her and her husband are known pacifists.
Hanstra drives Helen to her home in London and her husband Larry welcomes her back. The chauffeur takes the luggage and the golf bags into the house, while Larry admits that he can't go out with her that night because he has a project going on, and wasn't expecting her back so soon. Helen isn't happy with the news. A little later, a magazine calls to ask her to participate in a photoshoot. She agrees and goes to get her golf bag, but her butler Waring tells her that Hanstra left them in the car. Helen is sure that she saw Hanstra take them to the basement but when she tries to go downstairs, Hanstra comes out of the basement and tells her that he left the golf bag in the car. Once she walks off, Larry emerges from the basement and complains about how the two servants are treating Helen. Waring says that they have a lot of work to do and they all three leave.
When Helen comes back from dinner later, she hears noises from the basement. When she goes to check, Waring intercepts her and says that Larry hasn't returned yet from his project. Helen goes to bed and Waring joins Larry in the car where he's unloading the golf bag from the trunk of the car. The two men take the bag out and carry it inside.
Sir Charles drops Peter off outside the house, and gives the Invisible Man a radio to keep in contact with him. He then walks off so Peter has a vehicle, and Peter breaks into the garage. Peter watches as Peversham and Waring load several heavy bags into the trunk. Once they go back inside, Peter looks around and discovers that they have torn up Helen's golf bag.
Helen finds Larry in the study and asks her husband what's going on. He assures her that Waring and Hanstra are noble men and are taking risks for the safe of the world. Larry starts to tell her truth but then hesitates and tells his wife that she has to trust him. Helen reluctantly agrees and goes to bed.
Peter calls Sir Charles on the radio and tells him what he's found. Peter notices some tools inside the car and figures that Larry and Waring are moving something out that night. Meanwhile, Larry and Waring bring out more heavy bags. Helen is looking out her bedroom window and sees them, and is surprised when Larry drives off. Meanwhile, Peter gets in Sir Charles' car and follows Larry across the city.
Helen picks up the phone and starts to call the authorities, but then reconsiders and hangs up. Meanwhile, down in the basement Waring nervously paces in front of some radio equipment.
Larry pulls over next to an empty field and hauls the bags out.
Helen goes back to reading but hears a noise in the basement and goes to investigate.
After Larry leaves the sacks off and drives away, Peter checks them out and discovers that they contain pieces of cement. Realizing that Larry and his servants are digging in the basement and dumping the debris where it can't be traced back to them, Peter calls Sir Charles and has him bring in the police.
When she goes into the basement, Helen finds Waring, Hanstra, and two other men burying a nuclear bomb in the basement floor. They're talking about how Larry believes that they are part of a group placing similar bombs in other cities across the world, when they only plan to use the one in London for nuclear blackmail. Waring tells the other that they'll dispose of Larry once he's served his purpose. The butler arms the bomb and they plan to pour cement over it, but Waring catches a glimpse of Helen. She runs out of the basement, pausing to lock the door and delay them. They easily get through and capture her before she can call the police, and Waring tells the chauffeur to take her down to the basement and wait until Larry returns.
Once they take Helen back to the basement, Waring warns Helen that if she says anything to the authorities then they'll assume her husband knew what was going on. Realizing that the enemy agents will kill her no matter what, Helen refuses to cooperate. Larry arrives upstairs and Helen, hearing him, yells for him to call the policemen. Instead Larry comes into the basement and tells Waring that they can trust Helen. The butler has enough and shoots Larry, and Helen runs to her husband's side.
Peter pulls up at the same time as Sir Charles and the police and they all go inside. The enemy agents open fire but with Peter's help, the police easily capture them except Waring. The butler runs down to the basement and tries to set off the bomb, but Peter follows him and knocks him away from the detonator. The enemy agent tries to shoot Peter but misses, and Peter knocks him out as Sir Charles and the police run downstairs and capture the final enemy agent, saving London from a nuclear holocaust.