A Monday morning in August 1952. At Scotland Yard, Superintendent Folland inspects a letter posted the previous evening to the Prime Minister, and immediately travels to the Government Research Laboratory at Wallingford to find out all he can about its sender, Professor John Willingdon. Having interviewed Willingdon's fellow workers and family, Folland finally reveals to Stephen Lane, the Professor's assistant, the contents of Willingdon's letter: if the government doesn't agree to nuclear disarmament by noon the following Sunday, he will detonate a UR-12 bomb in the heart of London, laying waste to an area some 12 miles across.

Lane accompanies Folland to London, where the pair are interviewed by the Prime Minister. The Professor, meanwhile, leaves the derelict St Stephen's Westminster, where he has been praying for guidance, and takes a room at a boarding house run by Mrs Peckett. On Wednesday morning, disconcerted by his behaviour, Mrs Peckett summons the police. But Willingdon is out; on his return, he sees the police cars outside the house and heads off in the opposite direction. Having already had his identifying moustache shaved off, he next discards his mackintosh and goes to a pawnbrokers to buy an overcoat. There he meets 'Goldie' Phillips, a 'resting' soubrette of a certain age who offers him a bed in her Kennington flat.

The next day, as Folland's police dragnet continues the search for Willingdon, the Prime Minister finally makes a radio address to the nation, outlining the crisis and announcing that London will have to be evacuated and martial law instituted. Goldie announces her intention to leave for Aldershot but first informs Folland about the man she sheltered the night before. On her return home, however, she finds Willingdon's Gladstone bag, which contains the UR-12 bomb. Confronted by images of himself adorning every billboard and bus front, the Professor has been forced to return and proceeds to imprison Goldie in her own flat.

The mass evacuation follows on Friday, and on Saturday the army mobilises a house-to-house search of the deserted city, in the process discovering Goldie but not Willingdon, who has escaped over the Kennington rooftops. By Sunday morning, he is back in St Stephen's, where he is spotted by a squad of soldiers. Folland sends in Willingdon's daughter, Ann, to reason with him. When Folland and Lane get hold of the Gladstone bag, Willingdon flees down the aisle in confusion, only to be shot down by a panicky soldier at the exit. Lane defuses the device and the all-clear sounds at the stroke of noon.