English tourist Iris Henderson (Margaret Lockwood) along with her friends Blanche (Googie Withers) and Julie (Sally Stewart) arrive at the “Gasthof Petrus” inn in the country of Bandrika, “one of Europe’s few undiscovered corners”. Iris is returning to Britain to marry a “blue-blooded cheque chaser”, but an avalanche has blocked the railway line. The stranded passengers are forced to stay the night at the inn, including Charters and Caldicott, cricket enthusiasts who want to return to England to see the last days of the Test match.
Charters and Caldicott head for the dining room and are seated with Miss Froy (Dame May Whitty), only to find that due to the rush of unexpected guests, there is no food left. Miss Froy tells them of her experience being governess and music teacher for the past six years and now returning home to England. Upon hearing a folk singer in the distance, she remarks on the cultural richness of the country and exits the dining room.
In her room, Miss Froy opens the window to listen more intently to the folk singer, who sings on the street below her window. As evening comes, her listening is interrupted by a clarinet and stomping coming from the room above. Coming into the hallway of the inn, she encounters Iris, who has the room next to hers and is very perturbed by the noise. Iris calls the hotel manager, who enters the offending room to discover Gilbert Redman (Michael Redgrave), an ethnomusicologist, who is playing clarinet and transcribing indigenous folk music of the region while three natives dance. The hotel manager has Gilbert thrown out of his room. Gilbert attempts to make himself comfortable in Iris’s room, forcing her to capitulate.
As Miss Froy listens, the folk singer is strangled by an unseen murderer.
The next morning, before catching the train, Iris is hit on the head by a planter apparently aimed at Miss Froy, who then helps Iris onto the train. Also on board are Charters and Caldicott, Gilbert, a lawyer named Todhunter and his mistress “Mrs. Todhunter”. As a result of her injury, Iris blacks out. After the train is moving, Iris wakes up in a compartment with Miss Froy and several strangers. She joins Miss Froy in the dining car for tea. Unable to be heard above the train noise, the elderly lady writes her name on the window with her finger. Soon after, they return to their compartment, where Iris falls asleep.
When Iris awakens, Miss Froy has vanished. The strangers in her compartment say they know nothing about an English lady. Even Todhunter, who spoke with Miss Froy earlier, pretends not to remember her in an attempt to avoid any possible scandal. Iris searches, but cannot find her. She meets up with Gilbert, who agrees to help. Dr. Hartz (Paul Lukas), a brain surgeon, says Iris may be suffering from concussion-related hallucinations. Charters and Caldicott also claim not to remember Miss Froy, because they are afraid a delay would make them miss the cricket match.
Madame Kummer, dressed exactly like Miss Froy, appears in her place, but Iris and Gilbert continue to search. They are attacked by a knife-wielding magician, Signor Doppo. They start to suspect that Dr. Hartz’s patient, whose face is covered by bandages, is Miss Froy. Dr. Hartz tells his fellow conspirator, a British woman dressed as a nun, to drug Iris and Gilbert. Then, convinced they will soon be asleep, Hartz admits to them that he is involved in the conspiracy. The false nun does not follow Hartz’s instructions out of loyalty to her fellow countrymen; Gilbert and Iris escape, free Miss Froy and replace her with Madame Kummer.
When the train stops near the border, Dr. Hartz discovers the switch. He has part of the train diverted onto a branch line, where soldiers await. Gilbert and Iris inform their fellow passengers of what is happening. The train pulls to a stop and a uniformed soldier requests that they all accompany him. They knock him out and take his gun. Another soldier fires, wounding Charters in the hand, and a shootout begins.
During the gunfight, Miss Froy reveals to Gilbert and Iris that she is a British agent who must deliver a message to the Foreign Office in Whitehall. The message is encoded in the tune that the folk singer sang. Gilbert memorises the tune. With his help, Miss Froy slips away into the forest. Todhunter attempts to surrender, waving a white handkerchief, and is shot dead. Gilbert and Caldicott then commandeer the locomotive, and the group escape across the border.
In London, Charters and Caldicott discover the Test Match has been cancelled due to flooding. Seeing her fiancé from a distance, Iris avoids him and jumps into a cab with Gilbert. Recognizing that Iris would rather be with him than her betrothed, Gilbert kisses her. They arrive at the Foreign Office, and are seated in a waiting room. Suddenly Gilbert is unable to remember the vital tune. Gilbert and Iris then hear the tune on the piano. The doors of the office open to reveal Miss Froy playing the tune on the piano surrounded by ministers listening intently. The film ends as the three are joyfully reunited.