Dr. Arthur Calgary, a geophysicist recently returned from an Antarctic expedition, arrives one evening at Sunny Point, a house on the English coast. He has been dreading this visit all day. The day before, a lawyer named Mr. Marshall hinted that Calgary's "course of action" might have consequences beyond simple justice. At the house, a young woman named Hester Argyle tries to turn him away, assuming he is a journalist. Calgary produces Marshall's letter and is admitted to the library, where he meets Hester's father, Leo Argyle, a thin, scholarly man, and Leo's secretary, Gwenda Vaughan.
Calgary recounts the facts of a two-year-old murder. Jack "Jacko" Argyle came to Sunny Point demanding money from his adoptive mother, Mrs. Rachel Argyle, who refused. That evening, Mrs. Argyle was struck on the head with a poker and killed. Jacko's fingerprints were on the weapon, and money from her bureau was found on him. Convicted of murder, he died of pneumonia in prison six months later. Calgary reveals he was the stranger who gave Jacko a lift into Drymouth that evening, picking him up just before seven and dropping him well after half past seven, making it impossible for Jacko to have committed the crime. He explains his silence: after dropping Jacko, he was struck by a lorry, sustained a concussion, and lost all memory of that day. He left for the Antarctic and only recovered the memory weeks ago.
Instead of relief, Calgary meets wariness and silence. Kirsten Lindstrom, the family's Swedish live-in helper since Mrs. Argyle's wartime nursery in 1940, accuses him of upsetting everyone needlessly. As Gwenda ushers him out, Hester follows and says, "It's not the guilty who matter. It's the innocent." Leo telephones his eldest daughter, Mary Durrant, whose husband Philip Durrant uses a wheelchair due to polio, and his son Michael (Micky), who asks, "What's the betting? Which of us did it?"
Deeply troubled, Calgary returns to Marshall, who explains that since the house was securely locked, someone inside must have committed the murder. Jacko had been the convenient scapegoat, a problem child whose guilt was easily explained. Marshall provides background: Mrs. Argyle, born Rachel Konstam, could not have children and adopted five from disadvantaged backgrounds: Mary, Micky, Tina, Hester, and Jacko. Her wealth gave them a luxurious upbringing. Jacko had secretly married a young woman named Maureen; the family only learned of the marriage after his arrest.
Superintendent Huish reopens the investigation. The real killer likely overheard Jacko's quarrel with his mother and seized the opportunity. Suspects include Leo and Gwenda, who have a romantic relationship; volatile Hester; and Kirsten, who might harbor hidden resentments. Mary's alibi rests solely on Philip's word. A puzzle persists: Mrs. Argyle said she refused Jacko money, yet a traceable banknote was found on him. Huish theorizes someone gave it to Jacko as part of a frame-up.
Calgary conducts his own investigation. Maureen Clegg, Jacko's widow and now happily remarried, describes his charm and dishonesty. Tina Argyle, who works at a county library, distrusted Jacko and quotes Magna Carta: "To no man will we refuse justice." Dr. MacMaster, the retired local doctor, explains that Mrs. Argyle's unfulfilled maternal instinct made her over-protective and controlling. He observes that Jacko's pattern was not to commit violence himself but to incite others to act on his behalf.
The family gathers with Marshall for a legal conference. He advises them to present a united front, though he privately doubts the theory of an unknown intruder. That night, each member lies awake consumed by private fears. Philip resolves to investigate the murder, while Tina is troubled by something she knows now that Jacko has been cleared.
At Sunny Point, suspicion poisons every relationship. Kirsten warns Hester to trust no one. Leo hesitates about marrying Gwenda, devastating her. Hester's boyfriend, Dr. Donald Craig, presses her to confess to the murder so he can protect her. Hester admits she dreamed of killing her mother but refuses to confess to something she did not do. Craig's hesitation when she asks if he would believe her denial tells her everything.
Huish re-interviews the family, pressing each member on their movements during the narrow window between seven and half past seven. Hester accidentally reveals she knew when Jacko left, contradicting her earlier claim. Afterward, Tina says quietly, "I hope that I do not know anything." Philip begins probing family members, saying provocative things to gauge reactions. He talks Hester down from contemplating suicide at a window. Hester flees to London and seeks out Calgary, who tells her he is certain of her innocence. Philip interrogates Kirsten, who warns that his meddling puts him in danger.
New evidence surfaces: A village boy saw Tina's distinctive small red car near Sunny Point on the night of the murder. Tina admits to Huish she drove there but insists she did not enter the house. Calgary tracks down one of Jacko's former victims, a middle-aged woman he seduced and swindled, confirming his pattern of manipulating vulnerable women. Calgary suspects the key lies in Jacko, not as the murderer but as the instigator.
Tina finally reveals what she witnessed that night: She heard two people whispering outside the house, one saying "Between seven and seven-thirty. That's the time," and the other replying that "after that, darling, everything will be wonderful." She could not identify the voices. Shortly after confiding this to Micky, Tina drives to Sunny Point and finds Philip dead at his desk, stabbed through the back of the neck. Whatever he had been writing has been taken. Tina is then stabbed as well. Huish detains Micky after finding a bloodstained knife in his pocket.
Calgary pieces together the solution. Jacko's lifelong pattern was manipulating others into acting for him. Calgary gathers the household and reveals that Jacko targeted Kirsten, making her believe he loved her and would marry her. On the night of the murder, after Mrs. Argyle refused him money, Jacko instructed Kirsten to take the money from the bureau, then kill Mrs. Argyle with the poker while he established his alibi in Drymouth. Kirsten obeyed and staged a fake burglary. When the alibi failed and Jacko was convicted, she let him be punished, because the morning after the murder, Jacko's wife Maureen appeared at Sunny Point and Kirsten realized he had never loved her. With the case reopened, Kirsten killed Philip because his investigation was closing in, stabbed Tina because Tina had overheard the whispered plan, and planted the knife on Micky to frame him. Kirsten confesses.
Calgary explains Tina's cryptic words, spoken when she briefly regained consciousness: "The cup was empty" means Kirsten's coffee tray was a prop, since she had already killed Philip. "The dove on the mast" comes from a lullaby Kirsten sang to the children, which Tina associated with her attacker. Tina is expected to survive. Leo and Gwenda, freed from mutual suspicion, can pursue their relationship. Calgary believes Tina and Micky will marry, their bond deepened through the crisis. Hester tells Calgary she does not want to marry Craig, who never believed in her innocence; instead, she wants to marry Calgary, who always did. Surprised but certain of his feelings, Calgary accepts.