Murder Is Easy (1982)

A mathematician and author, Luke Williams, is travelling up to London on a train when he meets a old lady, Lavinia Fullerton, who is also going to London, to Scotland Yard. Lavinia tells Luke that in her small village several people have died. The local police are certain that it was all accidental and are taking no action but Lavinia isn't convinced. In London Luke watches, horrified, as Lavinia is run over in a hit and run and he becomes convinced that she was telling the truth. He travels down to the village and with the aid of a local girl, who is also convinced that the deaths were murder, sets out to solve the mystery.