In a central European country, an avalanche has delayed the departure of a train, forcing travellers on their way to England to stay overnight in a crowded hotel. Iris Henderson spends a last night with her friends before returning to London to marry a man she doesn't love. Old friends Charters and Caldicott are anxious to reach England for the last day of a test match. Iris's sleep is disturbed by Gilbert Redman, who is playing the clarinet in the room above. Investigating the noise she meets Miss Froy, an elderly governess. She bribes the hotelier to expel Gilbert, but when he proposes to take up residence in her room, she is forced to relent. Later, alone in her room, Miss Froy is serenaded from below her window by a man who is mysteriously strangled.

Boarding the train in the morning, Iris again encounters Miss Froy, and is hit on the head by a falling flowerpot. In the dining carriage, as Miss Froy and Iris introduce themselves properly, Miss Froy gives the waiter a special brand of herbal tea to prepare. The noise in the train is so loud that Miss Froy has to write her name in the condensation on the window. Returning to her compartment, Iris falls asleep. When she awakes, Miss Froy has disappeared. The other occupants of the compartment, including Signor Doppo, claim never to have seen Miss Froy and suggest that the blow to Iris's head must have confused her. Finding Gilbert and Dr Hartz, Iris searches for others on the train who may remember seeing Miss Froy, threatening to stop the train. Other passengers in the carriage deny having seen Miss Froy: Eric Todhunter because he is concerned at becoming involved in a scandal which will expose his adultery, while Charters and Caldicott are concerned that any delay may cost them their connection to England. Meanwhile, a bandaged patient, watched over by a nun, is put onto the train, to be operated on by Hartz at a hospital further down the line.

Signor Doppo announces that Miss Froy has returned, but when Iris returns to the compartment, Madame Kummer is in Miss Froy's seat, and Doppo and the Baroness claim she has been there all the time. Hartz suggests that Iris has become confused between Miss Froy and Madame Kummer. Deciding that she has been hallucinating, Iris goes for dinner with Gilbert, but notices Miss Froy's name written on the window. Agitated, she pulls the emergency cord and stops the train. Hartz suggests that she should disembark with him and his patient so she can be treated in hospital.

Gilbert sees Miss Froy's herbal tea packet being thrown out of the train, and becomes convinced something is afoot. He and Iris search the train and find Doppo's equipment, for his stage show as a magician. Doppo comes upon them and they fight, eventually securing him in one of his own trunks. But it has a false bottom and he escapes. They go to Hartz's compartment, finding only the bandaged patient and the nun. When they locate Hartz, Gilbert expounds to him over drinks in the dining car his theory that there is a conspiracy and that the bandaged figure is really Miss Froy. Hartz reveals that the patient is indeed Miss Froy but also that he is part of the conspiracy to kidnap and kill her. The drinks Iris and Gilbert have just had are laced with a drug, which will paralyse them. Iris and Gilbert pretend to pass out and Hartz leaves. Gilbert then climbs along the outside of the train to Hartz's carriage where he frees Miss Froy and the 'nun' reveals to him that their drinks in fact haven't been drugged. Kummer arrives but is overcome and bandaged to replace Miss Froy.

Hartz leaves the train with his patient but discovers it is Kummer in time to detach the carriages containing Gilbert, Iris and the dining English travellers from the train, sending it down a branch line. Soldiers approach and shoot Charters in the hand when he tries to leave the train. In the midst of the ensuing gun battle, Miss Froy announces to Gilbert and Iris that she must attempt to flee: she is carrying a secret message to London encoded in the tune the serenader played to her. She repeats it to Gilbert to remember, in case she doesn't survive. She runs into the woods behind the train, where she is shot at. Gilbert and Caldicott make their way across the top of the train and restart the engine, taking the train across the border into a safe country.

Back in London, Gilbert is still humming Miss Froy's tune. He and Iris prepare to part as Iris looks for her fiancé. When she sees him, Iris ducks into a taxi and she and Gilbert kiss. The taxi takes them to the Foreign Office but when they arrive, Gilbert has forgotten the tune. Despairing, they hear a piano playing the tune, and find that the pianist is Miss Froy, who has succeeded in making her escape.