In London, as American heiress Kit Preston struggles home through a dense fog, she is frightened by a disembodied voice that threatens to kill her. She races to the apartment she shares with Anthony, her financier husband of three months, where Tony dismisses the incident as a typical British practical joke, and distracts Kit by offering to take her on a romantic trip to Venice. The next day, Tony conducts a board meeting at which client Victor Elliott protests that someone has been devaluing his stock and then buying it out from under him. Tony, who is unaware that his treasurer, Charles Manning, carries large gambling debts, promises to investigate. When Kit arrives for lunch, Tony informs her that, once again, he must cancel their date in order to work. A gaunt stranger watches Kit as she returns to the apartment, where she is almost knocked down by a falling girder from the construction site that abuts the building. Contractor Brian Younger pushes Kit to safety, then alarms her by revealing that he knows her name. At home, Malcolm Stanley, the son of Kit’s maid Nora, visits and annoys Kit with his typical shiftless, unctuous behavior. As soon as he leaves, the threatening voice calls on the telephone, again claiming he will kill Kit. Her neighbor Peggy visits soon after and, noting Kit’s extreme anxiety, calls Tony. He brings Kit to Scotland Yard, where Inspector Byrnes questions her but surreptitiously suggests to Tony that her fears may be the hysterical invention of a lonely housewife who wants her husband’s attention. Soon after, Kit prepares to go out with her beloved aunt, Bea Coleman, who is visiting London. Although Bea’s presence calms her, Tony further upsets Kit by canceling their Venice trip in order to take care of a business emergency. Just then, the phone rings again, and although Tony tries to listen in, before he can hear anything, Kit hangs up, unable to endure the caller’s vile words. They meet Bea and Charles, her old beau, at a nightclub, where Bea questions Tony about Kit’s agitation. After Tony mentions Byrnes’s suspicion, Bea also wonders if Kit could be inventing the threats. The next day, Kit is in the apartment building elevator when it becomes jammed. The sound of footsteps approaching the dark car causes her to panic, but it is only Brian, whose construction work has disrupted the building electronics, attempting to rescue her. He takes her to a local pub, where he commiserates with her panic by describing his experience while trapped in a burning tank during World War II. His intensity makes her uneasy, and she returns home. A few days later, Kit, Tony, Bea and Charles attend the ballet, but Tony is called to the office by his assistant, Daniel Graham, who has discovered that someone has embezzled one million pounds from their business accounts in order to buy out Elliott. At the same time that Daniel, who covets the position of company treasurer, suggests that Charles is the culprit, Malcolm slips into Kit’s box at the ballet to pester her for money, and vaguely threatens her when she demurs. Over the next few days, Kit becomes increasingly paranoid, but none of her suspicions amount to anything. One day, however, a threatening call is followed by a visit by the gaunt man, and when Kit screams, Brian hears her and races into the apartment. No intruder can be found, and after Byrnes is called, he once again doubts Kit’s story. Later, Tony promises to take Kit away to Venice, but the next day, she spots the gaunt man in the street and soon after is pushed in front of a bus. Kit is unhurt but frantic, and after Peggy helps her inside, she begs her neighbor to lie to Tony that she has heard the voice on the phone. Peggy reluctantly complies, but Tony reveals that the phone has been out of order all day. He then invites Bea over and secretly reveals Kit’s fib. When the phone then rings, Kit insists that Bea answer and pretend to be her, but Bea is dismayed when she hears the voice ask what time Kit wants him to call her. Now convinced that Kit is delusional, Tony and Bea send her to a psychiatrist, who suggests she may have a split personality. Tony decides to take Kit to Venice the following day, and later, while she is packing, calls Bea to stay with Kit while he attends a board meeting. Before he leaves, the voice phones again, and when this time Tony hears it, he phones Byrnes to ask him to surround the building. While Tony formulates a plan to appear to have left the building, thus enticing the man to attack, outside Brian spots the gaunt man and tails him. Tony leaves briefly, then returns in secret. Just then, the caller phones to announce that he is coming to kill Kit. In the dark, a man enters with a gun drawn, and Tony tackles him to the ground. After a struggle, Tony emerges victorious, but suddenly turns on Kit and admits that he and Peggy have conspired to make the threatening phone calls. They now plan to kill her, making her death appear to be an hysterical suicide, in order to collect her inheritance, which Tony will use to repay the million pounds he has stolen from his business. Just as Tony attacks Kit, the gaunt man reveals himself to be Peggy’s absent husband Roy, who has discovered her affair and wants to murder her. Kit races to the door, where she discovers Byrnes, who reveals that he had tapped the Prestons’ phone and heard Tony make a fake phone call to the police. While Byrnes arrests Tony and Peggy, Brian and Bea lead Kit to safety.