Christine Clay (Pamela Carme), an actress who owes her career to her husband, is severely criticized by him for playing around with other men. He makes particular reference to Robert Tisdall, a young man staying with (or at least near) them at their country retreat somewhere on the English coast. One night, Christine smacks her husband in the face. He keeps calm except for his eyes, which twitch uncontrollably, then proceeds to strangle her with the belt from a trenchcoat he has stolen. For some reason, he is not suspected by the police.
Robert Tisdall (Derrick De Marney) happens to be walking along the seaside cliffs when Christine's body washes ashore. A belt is found next to the body. He runs to get help or call the police and is seen doing so by two young female swimmers. He is arrested and becomes the main suspect. His motive seems to be a large sum left to him in her will. Saddled with a hopelessly inadequate barrister, Tisdall doubts if his innocence will ever be established. He makes his escape in the crowded courthouse corridor.
Tisdall gets a lift from Erica Burgoyne (Nova Pilbeam), daughter of the local police Chief Constable, in her dilapidated Morris car. They are spotted together, so the police suspect she is his accomplice. Tisdall tries to prove his innocence by tracking down the stolen coat.
During their flight, they briefly stop at the home of Erica's aunt, where her seven year old daughter Felicity is having a birthday party (playing, among other games, Blind Man's Buff). Finally, in a lodging house frequented by tramps, Tisdall finds the man he has been searching for: Old Will (Edward Rigby), a sociable china-mender who is wearing Tisdall's coat. He agrees to help them find the man who gave him the coat, and thus clear Tisdall. Unfortunately, the twitching eyes are all that Old Will can remember about the man.
In a pocket of the coat, they find a box of matches from the Grand Hotel, a place Tisdall has never been to. They go there in hopes of finding the murderer. In a memorably long, continuous sequence, the camera moves forward through the hotel ballroom to finally focus on the drummer in a dance band performing in blackface. Recognizing Old Will in the audience, and seeing policemen nearby (unaware that they are there to arrest Tisdall), the man performs poorly due to fear and is berated by the musical conductor. Then he has a nervous breakdown, exacerbated by a drug he has been taking to try to control the twitching, and passes out. Immediately after being revived, he confesses his crime and laughs. In the end, Robert Tisdall and Erica Burgoyne are united, with Erica's father smiling benevolently.