The Doctor and Donna Noble arrive in Britain in the 1920s and in particular at a garden party. The Doctor uses his telepathy ID card to avoid suspicions of being an unwanted guest which he is. The garden party includes famed British crime writer, Agatha Christie. It just happens to be right about the time that Agatha Christie disappeared in real life. The episode plays homage to the board game Cleudo with Professor Peach instead of Professor Plum who gets murdered in the library with a lead pipe.
The Doctor, Donna and Agatha set about investigating the murder. Donna is first to discover a giant Wasp that attacks her when she enters a room that has been closed for forty odd years on the orders of the lady of the house, Lady Clemency. During the investigation, the Doctor is poisoned by cyanide. In one of Agatha's books, the victim is killed by being poisoned by cyanide. However unlike the victims in the books, the Doctor is able to come up with an antidote and save himself.
The Doctor and Agatha Christie calls them all to the lounge and together the duo reveal who is being the crimes. They reveal that the Unicorn in the title, a criminal thief is Robina Redmond but is not the murderer. Robina is played by Felicity Jones who would go on to play Jyn Erso in the star Wars anthology film, Star Wars - Rogue One.
The Doctor reveals that Lady Clemency who had locked herself away in her room forty years ago, was because he was pregnant at a time that unmarried pregnant women were frowned upon. When the baby was born, the child was adopted. It was revealed that the father was a Vespiform who she had fallen in love with many years ago. A Vespiform was a creature that was a giant wasp but could disguise himself as human. They reveal the Vespiform is the vicar who had come back to see him mother.
When the vicar turns into a wasp, they leave the room and Agatha runs out and gets into a car and drives away. The doctor follows and it soon becomes clear why Agatha disappeared for ten days without any recollection. The Doctor takes Agatha to where Agatha would later turn up in real life.