Morse and Lewis are called to a pub outside Oxford where a young woman named Sylvia Kane has been found dead in the car park, seemingly run over but with scratches on her face that suggest an attack. An envelope is found in Sylvia's purse, addressed to her superior at work, Jennifer Coleby, and containing what Morse identifies as a coded letter. Inquiries begin at the Oxford assurance company where both women worked. Morse presumes the envelope contained a large quantity of cash. The young man Sylvia was meeting at the pub begins to spend money in an extravagant fashion, soon gets into trouble and is brought into the station. He admits that he took the money and Sylvia's necklace after discovering her body, but despite this confession, Morse is not convinced that he killed her and lets him go.
Mrs Jarman, an elderly woman who recognised Sylvia on a television appeal hosted by Morse, contacts the police and says she saw Sylvia get into a red car at a bus stop on the night in question. She mentions that another person was with Sylvia but did not get into the car. Sylvia departed with the words, "See you in the morning." A few days later, Mrs Jarman sees the same car, which had a broken tail light, and notes the registration number. The car is registered to Margaret Crowther, wife of Dr Bernard Crowther, an Oxford don whom Morse recently heard give a lecture.
Dr Crowther was driving the car the night of Sylvia's death and has admitted to his wife that he picked her up, stopped for a drink with her, and took her to the pub where her body was found. He claims that she came on to him, and when he rejected her, she became angry and left the car. He says that when he backed his car out he felt "a slight bump", which he thought was a curb, and drove home. His wife refuses his desire to contact the police and confess, because he is in line for a prestigious professorship.
Crowther has a heart attack while he and his wife are disposing of evidence from her car. When Morse and Lewis arrive at the Crowther home to question him, they are surprised to encounter pathologist Max, who is Mrs Crowther's uncle. In discussing the Kane case, Max mentions that she'd previously injured her elbow and had an therapy appointment the hospital the day after her death. Remembering how Sylvia had said "See you in the morning" to her companion, Morse realises that it must be someone who works at the hospital. Lewis suggests it could be the nurse who lives in Jennifer Coleby's home, Mary Widdowson.
Widdowson confesses the truth to Morse. She and Crowther were having an affair. He wanted to avoid any possibility of scandal while under consideration for the professorship, so he sent her the money to take a holiday and be absent for a while. The money was to get to her via Coleby, but Sylvia Kane intercepted it. When Sylvia was coincidentally picked up by Crowther at the bus stop, Mary Widdowson did not get in. Instead, she followed them on the bus to see what would happen between them. When Sylvia got out of the car at the pub, Mary confronted her and knocked her to the ground. Crowther inadvertently ran over her as he reversed out of the car park. Although the death was not murder, Widdowson is led away by the police for her hand in it, as Crowther regains consciousness in his hospital bed.