A blind playwright living in London overhears part of a conversation that propels him into a desperate race to find a kidnapped child.

Phillip Hannon, a successful playwright whose recent blindness has driven him to move from New York to London, is paid a surprise visit one day by Jean Lennox, the woman to whom he was once engaged. Phil, bitter and self-pitying since losing his sight, abruptly dismisses Jean and then leaves the apartment. In Phil's absence, Jean tells his secretary, the devoted Bob Matthews, that Phil broke their engagement after becoming blind. Phil walks to the Eagles Bar, and while slumped in a booth there, overhears a muffled conversation between a man named Evans and a whimpering woman, in which Evans browbeats the woman to agree to do a disagreeable task on the 10th of the month. Obsessed by the encounter, Phil returns home, dictates the couple's dialogue into his tape recorder, and then summons the police. With the 10th just a week away, Phil speculates that kidnap or robbery may be involved, to which Inspector Grovening responds that Phil is suffering from an overactive imagination. Afterward, Phil recalls the scent of perfume worn by the woman and ascertains its name. To humor Phil, Bob and Jean join his search for the reluctant woman. When Phil recalls her stating that she took the #73 bus and that she worked for nobility, they spend the night pouring over the peerage books for names of Lords with small children who live in the Knightsbridge area. The next morning, Bob narrows the list to Lady Syrett. Upon discovering that Lady Syrett's nurse is named Janet Murch and that she works for the Unity Domestic Bureau, Phil sends Jean to the bureau posing as a prospective employer. When Jean asks about Janet, the bureau's head, Mr. Pilling, becomes suspicious and asks for Jean's address. Rattled, Jean provides him with Phil's address, and soon after, a woman identifying herself as Miss MacDonald comes to apply for a job. After a brief interview, the woman leaves, and Phil, recognizing the scent of her perfume, sends Bob after her to take her picture. Trailing the woman to a department store, Bob buys a camera, and then returns home hours later, tired and wet, with the news that although he snapped her picture, he lost her once she entered a deserted house. When Lady Syrett states that the woman in Bob's photo is not Janet, Phil, frustrated, lashes out at Bob and Jean and then decides to place a classified ad in the paper asking Janet to call his phone number. Soon after, a shadowy figure at a bar pays a drunken woman to impersonate Janet and ascertain Phil's name. Meanwhile, the real Janet, in a quandary, decides to call Phil from a phone booth near the river. As Phil answers the phone, Evans appears at the booth and forces Janet to arrange a meeting with "her father" in one hour at the Eagles Bar. After Janet hangs up, Evans stabs her and tosses her body into the river. One hour later, a man enters the Eagles Bar and introduces himself to Phil as Murch. Although Phil pretends that he can see, the man realizes that he is blind and offers to take him to Janet. After Murch escorts Phil out of the bar, Bob arrives and tries to follow them. Leading Phil into a partially demolished building, the man locks him in a room that has no back walls. When a portion of the floor collapses, Phil senses that he is in danger and calls for help. Hearing his cries, Bob locates Phil and comes to his rescue. Back in the safety of his apartment, Phil tells Jean that his brush with death made him recognize that he still cares about living. After Janet's body is found in the river, Inspector Grovening begins to seriously consider Phil's story. As the morning of the 10th arrives, Phil, feeling responsible for Janet's death, becomes consumed with preventing the planned crime. While replaying the tape once more, Phil realizes that the name Mary really refers to the ocean liner the Queen Mary , which docked that morning in London. With the help of the police, Phil checks the passenger list for wealthy couples traveling with children. When the De Mesters, a wealthy Argentine couple with a seventeen-year-old daughter, appear to be the only candidate, the police hurry to their hotel and learn that their retarded daughter has disappeared with her nursemaid. After a search of the area turns up the girl's wheelchair and her doll, Phil smells perfume on the doll and, associating it with MacDonald, insists that the police search the empty house to which she led Bob. Later, the police phone Phil with the news that they have found the child and two of her kidnappers, but that MacDonald was not among them. When the phone line goes dead, Phil senses that danger is near and deliberately insults Jean to drive her from his apartment. Hearing noises outside his doorway, Phil hurriedly records several greetings to Evans and then smashes all the light bulbs, throwing the apartment into darkness. When Evans slips in through the back door, Phil plays the recordings, thus disorienting his attacker. Catching Evans off guard, Phil wrestles him onto the stairway, where he loses his balance and falls to his death. The police and Bob arrive soon after, and when they turn over the body, they find that it is MacDonald, dressed in men's clothes. The next day, Phil tenderly caresses Jean's face and then kisses her.