As the American heiress Kit Preston navigates the fog-laden streets of London's upscale districts, she is unexpectedly confronted by a chilling, disembodied male voice threatening to take her life. The next day, her husband Tony, a British business owner, learns from his assistant Daniel Graham that a large sum of money has gone missing from their company. Upon returning home, Kit encounters a gaunt figure who seems fixated on her, and she narrowly avoids danger when a falling girder almost strikes her, thanks to Brian Younger, a contractor involved in the renovation.
The following day, Kit gets another menacing phone call from the same voice, this time with an even more sinister threat. As her anxiety spirals, her neighbor Peggy becomes concerned and reaches out to Tony, who arrives quickly to take charge. They visit Scotland Yard, but Inspector Byrnes dismisses her fears as mere attempts to garner attention. Comfort comes in the form of Kit’s aunt Bea Coleman, who provides reassurance as Kit spills her troubling experiences.
Due to Tony's business commitments, he reluctantly cancels their anticipated trip to Venice, which only adds to Kit's frustrations. Instead, another disturbing call comes in, which Tony tries to intercept but fails to prevent Kit from hanging up amidst the abuse. The following day proves disastrous when Kit finds herself stuck in a malfunctioning elevator, frantically pressing buttons until Brian appears from above, trying to assist.
Days later, Kit and Tony attend a ballet performance with Bea, along with Malcolm, the son of their maid Nora, and Charles Manning, treasurer of Tony’s company. During the performance, Malcolm hints at needing more financial assistance for his mother, but Kit assures him that she will ensure Nora is well cared for. Tony, however, suspects Malcolm might be linked to Kit's menacing phone calls.
As days drift by, Kit is overwhelmed with paranoia. The unsettling gaunt figure materializes once again in her home, causing her to scream in horror. Although Brian rushes to help her, the police find no evidence of intrusion. The next day, she once again spots the gaunt man, only to be shoved into the path of an oncoming bus, narrowly escaping demise.
In a desperate bid for support, Kit implores Peggy to simulate a call from the stalker, in hopes of convincing the authorities of her claims. But when Tony announces the phone has been disconnected all day, her reality begins to crumble. Convinced of her instability, Tony and Bea decide to take her to see a psychiatrist.
With Tony scheduled for a business trip to Venice, the elusive caller strikes yet again. Byrnes encircles the apartment building when Tony pretends to leave, while Brian decides to follow the gaunt figure to unravel the mystery behind him.
As Kit’s world collapses, she is startled to find the gaunt figure in her dark apartment, only to be saved by Tony, who claims to have thwarted the threat. Yet, as Kit basks in this fleeting sense of safety, Tony’s sinister plot reveals itself: he and Peggy have conspired to torment Kit, intending to stage her demise as a suicide to inherit her wealth and settle his business debts.
In a twist of fate, the gaunt man's true identity is unveiled as Peggy's estranged husband, out for vengeance over her affair with Tony. With Tony’s deceit laid bare, Kit seizes the chance to escape, navigating precarious construction girders along the balcony and eluding capture. Just in time, Brian comes to her aid and helps her back inside, where Byrnes discloses his findings of Tony’s malfeasance after monitoring their phone calls.
