Jane Marple, the elderly amateur sleuth, takes a holiday at London's Bertram's Hotel, a place of which she has fond memories from her youth. The establishment has retained a mixed Edwardian and Victorian atmosphere, from its prim staff to its elderly patrons. In its tearoom Miss Marple encounters a wartime friend, Lady Selina Hazy, who reveals that she frequently thinks that she recognises people in the hotel only for them to turn out to be complete strangers. Miss Marple is intrigued by her fellow guests, who include the famous adventuress Bess Sedgwick, 17-year-old Elvira Blake and her legal guardian Colonel Luscombe, and a forgetful clergyman, Canon Pennyfather.
Elvira's late father bequeathed her a large sum of money, to be held in trust until she is 21. Her mother had abandoned her as a baby to pursue her career and the two are estranged. Having questioned her guardian on who would inherit her money if she were to die, Elvira hints she is planning marriage. She also claims someone had once tried to poison her during her school days in Italy. Flying in secret to Ireland for the day, Elvira confides in her best friend, Bridget, that she has to discover something of great importance, but is not specific.
On the same day that Elvira travelled to Ireland, Canon Pennyfather had arranged to attend a conference in Lucerne, Switzerland. However the confused cleric arrives at the airport a day late, missing his flight by a full 24 hours. He returns to Bertram's around midnight, disturbing an intruder in his bedroom. Having been knocked unconscious he awakens four days later in a house several hours from London, but near the location of a recent robbery of the Irish Mail train. A family had found him on the side of the road and taken him in. Pennyfather is able to recall nothing since taking the taxi to the airport, yet some witnesses of the robbery state they saw somebody resembling the canon. Miss Marple also witnessed him departing his hotel room at 3 am, three hours after he was assaulted, and a few hours before the robbery.
It becomes clear that Bess Sedgwick had distanced herself from her child, Elvira, because she did not consider herself a suitable mother. However, they do share a taste in men, being lovers of the same man, the French/Polish/Italian racing driver, Ladislaus Malinowski. A car similar to one driven by Malinowski seems to be connected to the robbery of the Irish Mail, and to several other recent robberies.
Miss Marple overhears Bess Sedgwick talking with the hotel commissionaire, Michael "Micky" Gorman. It turns out they had once been married in Ireland. At the time, Gorman had told her the wedding was just a game and not a legal marriage. But their union was genuine, and her four subsequent marriages were unwittingly bigamous. Later on, outside the fogbound hotel two shots ring out, followed by screams. Elvira Blake is discovered next to the corpse of Gorman. The young woman claims he has been shot dead after he had run in front of her to shield her from the gunfire. The gun is Malinowski's.
Police Chief Inspector "Father" Davy, along with Inspector Campbell, has been involved in the mystery since Pennyfather's disappearance. He interviews everybody in the hotel, and quickly realises that Miss Marple notices things– things in human nature that provide important clues. After Pennyfather is found, the three of them attempt an experiment. Miss Marple persuades the clergyman to re-enact his likely movements from the point when she believes she saw him in the hallway, movements that Pennyfather cannot recall. Whilst watching him walk down the hallway she realises it wasn't him whom she saw. Pennyfather's memory is jogged; he remembers he saw himself sitting on a chair, just before he was knocked unconscious. His doppelgänger, with his confederates, must have left the hotel with the supine canon and driven to the mail train. Pennyfather was thereby framed for the crime.
Miss Marple confides in Inspector Davy her disappointment in Bertram's atmosphere of fakery. She acknowledges that the past cannot really be revived, although the staff are expert. Although some guests are genuine, others seem to be acting or pretending to be what they are not. Had Lady Selina been right? Were the people she recognised imposters? It dawns upon Marple and the inspector that the hotel is being used by a criminal gang. The actors pose as other people during robberies to provide alibis for their cohorts.
Davy and Miss Marple confront Bess Sedgwick as the orchestrator of these robberies, along with the hotel's owners and staff. Sedgwick confesses not only to this, but also to the murder of Michael Gorman. Making a run for it, Bess steals a car and speeds away recklessly, crashing fatally. Miss Marple is not convinced Sedgwick really killed Gorman, and believes she said so to protect the real murderer, her daughter Elvira. Elvira had also overheard the conversation between her mother and Gorman about their marriage, and realised it made Sedgwick's marriage to Elvira's father invalid, and Elvira illegitimate. Elvira's main concern was that, under the terms of her father's will, she would be barred from inheriting his estate by this fact. This would lose her not only the money, but also the attention of Ladislaus Malinowski: she loves him, but recognises his main interest is her wealth.