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During World War II in England, inmate Stephen Neale is released from an asylum after having served a two-year sentence for killing his terminally ill wife.  Stephen buys a train ticket to London, but before the train departs, he is drawn to a nearby charity fête being held by the Mothers of Free Nations.  Stephen buys a ticket for a cake weight-guessing contest, then on the advice of fortune-teller Mrs. Bellane, Stephen buys a second ticket and correctly gives the weight of the cake.  Stephen wins the cake, but before he exits the fête, a man in a black coat rushes into Mrs. Bellane's tent, and Stephen is told his guess was wrong after all.  As Stephen's first guess was still closest to the true weight, he jubilantly boards the train with his cake.  Stephen is joined in his compartment by a blind man, with whom he shares the cake, but does not notice when the man momentarily breaks his glazed look to watch him.

When the train comes to a stop due to a bombing raid, Stephen looks out the window, and the blind man hits him over the head with his cane, then runs out of the compartment clutching the cake.  The man shoots at Stephen as he chases him across the misty moors, but perishes when a bomb drops on the cottage in which he has taken refuge.

Later in London, Stephen hires Mr.  Rennit, an alcoholic private detective, to help him investigate the Mothers of Free Nations organization.  Austrians Willi Hilfe and his beautiful sister Carla run the charity, and agree to help Stephen after hearing his story.  Rennit follows Willi and Stephen to Mrs. Bellane's house, but Stephen is shocked to find that the glamorous woman calling herself Mrs. Bellane is not the same as the fortune-teller at the bazaar.  Mrs. Bellane invites them to join a séance, whose other participants include psychiatrist Dr. Forrester, artist Martha Penteel, and Mr. Cost, whom Stephen recognizes as the black-coated man at the fair.  After the room darkens, Mrs. Bellane seems to speak as Stephen's dead wife and accuses him of murdering her.  After Stephen becomes hysterical, Cost is shot to death, and Stephen is accused of his murder.

Willi helps Stephen escape, and by nightfall, Stephen discovers that Rennit's office has been ransacked and that he has disappeared.  Stephen then meets Carla alone during an air raid, and reveals details about his previous crime: Stephen's terminally ill wife begs him to end her misery, but when he is unable to administer the poison he has bought, she takes the poison herself.  Stephen is found guilty of mercy killing and is incarcerated in an asylum.  Carla is compassionate toward Stephen and the next day takes him to hide at her friend Newland's bookshop.  After picking up Forrester's book, The Psychology of Nazism, and learning that Forrester is an advisor to the Ministry for Home Security, Stephen suspects that Carla's organization may be a front for spies.

Carla, meanwhile, returns to her office to search the card files for all the names affiliated with the organization, while Stephen learns from Mrs. Bellane that she used published information about his trial for the séance, and admits that it was not she who gave him the cake's correct weight.  Carla then identifies several people enrolled in the charity as possible German spies and confides her fears to Willi.  Willi urges her to stay away from Stephen, but Carla confesses that she has fallen in love with him.

Later, Carla and Stephen become engaged and deliver some books for Newland to Forrester.  When they are let into an empty apartment, the suitcase in which they are carrying the books explodes.  Stephen awakens alone some time later in a hospital, and is interrogated by Prentice, a Scotland Yard inspector who has been following him.  Stephen refuses to reveal Carla's identity in order to protect her.  Prentice, who has arrested Stephen for Rennit's murder, doubts Stephen's story of a spy ring, but agrees to search the site where the blind man died.  After an exhaustive search of the moors, Stephen finds a small tube of film embedded in a chunk of cake.

At the national Ministry for Home Security, the film is revealed to be the new defense plans for the Channel, which had only been taken out of the vault twice before, once while Forrester was present.  Defense agents now realize that Travers, a tailor recommended by Forrester, was the only civilian at the Ministry the previous day, and that the apartment where the bomb exploded was leased in his name.  Prentice goes to Travers' shop for a suit fitting, and when Stephen arrives five minutes later, he recognizes Travers as "Cost," who he thought was dead.  Cost pretends not to recognize him, and after making a phone call, escapes into another room and stabs himself to death with a pair of shears.  While a crowd gathers around Cost, Stephen telephones the number of Cost's most recent suit delivery and recognizes Carla's voice at the other end.  Stephen goes to their apartment, where Willi takes both him and an innocent Carla hostage, and admits that he has been trying to get rid of them because they know too much about the spy ring.  Stephen realizes that the most recent film is sewn into the suit, and attacks Willi.  Carla kills her disloyal brother during the struggle and escapes with Stephen onto the roof.  After exchanging gunfire with Forrester, he and his entourage of Nazi spies are killed by British police.

Some time later, Stephen and Carla plan their church wedding.