In an "uncivilized" Alpine region of pre-World War II Europe, the return to good old England of a motley group of tourists eager to get back home is delayed by an avalanche blocking the rail tracks. Among the passengers are Gilbert (Michael Redgrave), a young musicologist who has been studying the folk songs of the region; Iris (Margaret Lockwood), a young woman of independent means who has spent a holiday with some friends but now has to travel home alone on some urgent business; and Miss Froy (Dame May Whitty), an elderly lady who is returning to England after years abroad as a governess.
When the train can continue its journey, Iris and Miss Froy, who happen to sit in the same compartment, strike up a conversation, while the remaining passengers seem to be natives unable to understand a word of English. When, in the course of the journey, Miss Froy vanishes into thin air and Iris voices her concern about the old lady's disappearance, she is shocked to learn that all the other passengers claim Miss Froy never existed.
Warning: Wikipedia contains spoilers
Everyone, including a foreign doctor, declares that she must be hallucinating due to a minor accident on boarding the train. Unwilling to be fooled, Iris starts to investigate and is joined in her efforts to discover Miss Froy's whereabouts only by Gilbert, with whom she eventually falls in love.
Soon the couple find out that it is really evil forces that are at work here. Miss Froy has been kidnapped and is being held prisoner in a sealed-off compartment which, it is alleged, is occupied by a seriously ill patient on his way to be operated on. After the car carrying the protagonists has been uncoupled, detoured and brought to a standstill on an unused piece of track, a shootout ensues. Miss Froy confesses to Gilbert and Iris that she is in fact a British spy assigned to carry classified information to the Foreign Office in London; after entrusting her message, which has been encoded in a folk song, to Gilbert, she attempts to escape under cover of the shootout.
After making their own escape from the villains, Gilbert and Iris return to London with the message. At the Foreign Office, Gilbert, driven to joyful distraction - he has proposed to Iris, and she has accepted - discovers that he can't recall the tune. Fortunately, Miss Froy has also made good her escape, and is able to complete her mission herself.
It must be noted that the plot of Hitchcock's film differs considerably from White's novel. In The Wheel Spins, Miss Froy, who really is an innocent old lady looking forward to seeing her octogenarian parents again, just has the misfortune to witness a murder shortly before boarding the train. In White's novel, the wheel keeps spinning: The train never stops, and there is no final shootout.
It has often been stated that the action of the movie is set in Nazi-controlled Austria immediately before the outbreak of the Second World War, although the film itself gives no such specific information about the setting.
Two of the supporting characters in the film, the rather dim-witted cricket fans Caldicott and Charters (played by Naunton Wayne and Basil Radford), were very popular with audiences, so much so that this pair of characters starred in a movie of their own, Crook's Tour (1939), and appeared as supporting characters in two more Gilliat-and-Launder-scripted movies, Night Train to Munich (1940) and Millions Like Us (1943). They were resurrected again for a BBC television series, Charters & Caldicott, in 1985, starring Michael Aldridge as Caldicott and Robin Bailey as Charters.
The Lady Vanishes was remade in 1979. It was directed by Anthony Page and adapted by George Axelrod. It stars Elliott Gould as Robert (Gilbert), Cybill Shepherd as Amanda (Iris), Angela Lansbury as Miss Froy, Herbert Lom, Arthur Lowe and Ian Carmichael.