This film had a long gestation. It began life as a play by Frank Launder and Sidney Gilliat called "The Body Was Well-Nourished", originally written in 1937, but not staged until 1940. At that time, the character of the assassin was a supporting role. The play lasted less than three weeks in London, although this was less due to unpopularity than to the Blitz. Launder and Gilliat were never quite satisfied with the play, and, after the war, revised and updated it, retitling it "Meet A Body". This was first staged in 1954 (produced by Laurence Olivier, who did not act in it), but the authors still felt it could be improved, and turned it into a film vehicle for Alastair Sim, who originally wanted to direct, or at least co-direct, it. He had some disagreements with Robert Day, so several scenes were directed either by Basil Dearden or by Launder and Gilliat themselves.
The surnames used by Alastair Sim's character--Hastings, Ramsgate, Margate--are all names of coastal towns on the southeast coast of England.
The scene in which George Cole tries to phone the police and Alastair Sim tries to stop him was improvised.
"Meet A Body", on which this is based, was Launder and Gilliat's only play, running at London's Duke Of York Theatre for fourteen weeks from July 21 1954.