West London, the early 1940s. Pretending to be able to cure her bronchitis, John Reginald Christie lures Muriel Eady into his house at 10 Rillington Place, where he puts her to sleep with a cocktail of carbon monoxide gas and other chemicals before strangling her.

In 1949, Timothy and Beryl Evans and their baby daughter Geraldine move into two rooms on the top floor of 10 Rillington Place. When Evans is at work, Christie tells Beryl that he would be happy to offer free medical advice. Beryl is unnerved by Christie, and is relieved when her friend Alice pays her a visit.

Christie shows Evans a letter saying that Beryl is six weeks in arrears on their furniture payments. The illiterate Evans was unaware of this, and has a loud argument with Beryl. Beryl tells him that she's pregnant, but has already attempted a self-induced abortion by taking some pills. The argument wakes both Christie and the neighbours.

The next day, Christie talks to Beryl about her pregnancy, and says that he knows how to perform an abortion. She discusses this with a reluctant Evans, who is eventually persuaded that they cannot afford to support another child.

The next morning, Christie reassures Evans that he knows what he's doing, but warns him that there's a 10% fatality rate. After Evans goes to work, Christie invents an excuse to get his wife out of the house. He goes to Beryl's room and begins gassing her, claiming that it's an anaesthetic. Beryl starts to struggle and scream, so Christie knocks her unconscious. He caresses her body and climbs on top of it, rope in hand. He has just finished strangling Beryl when he hears Alice coming up the stairs. She knocks at the door, but eventually goes away.

Evans returns home, to be told that Beryl has died. Christie says that he will probably be charged as an accessory to criminal manslaughter, unless he helps him dispose of the body. Evans wants to call the police, but Christie says the neighbours will think that Evans killed his wife during one of their rows. He advises Evans to go away for a few days, offering to put Geraldine up with a childless couple in Acton. After Evans leaves, Christie goes upstairs and strangles Geraldine.

Evans returns to his native Wales visit Mr and Mrs Lynch, his aunt and uncle, claiming that his car broke down in Cardiff while he was on business, and that Beryl and Geraldine are staying with her father. A few days later, his aunt receives a telegram from Beryl's father, wondering where they are. Evans claims that Beryl went off with another man.

Evans goes to the police station and confesses to disposing of Beryl's body down a manhole following her accidental death after drinking something to procure an abortion. When the facts are challenged, Evans changes his story, saying that he was only trying to protect Christie.

Christie shows policemen round, saying that Beryl wasn't very good with money and she was constantly fighting with Evans. They find the bodies of Beryl and Geraldine hidden under the outhouse sink.

The police take Evans back to London, where they break the news of Geraldine's death. He is charged with murder.

At the trial, Christie denies knowing anything about the murders. The defence counsel brings up a string of previous convictions for theft and violence, but he is commended for his service in both world wars. Evans is unable to explain why Christie should have murdered his wife and daughter, and he is duly found guilty, sentenced to death and hanged.

Two years later, Mrs Christie complains that they are financially struggling because no-one will occupy the rooms following the Evans murders. She makes it clear that she suspects her husband.

Christie sells his furniture, claiming that his wife has gone to Sheffield. He stays in a doss-house, where he tells people about his involvement with the Evans case.

In Rillington Place, removal men discover the bodies of Christie's wife and his other victims behind some freshly-applied wallpaper. A policeman recognises Christie and arrests him. He is later hanged for his crimes, and Evans is formally pardoned.