They Can't Hang Me (1955)

Sentenced to death for murder, a civil servant reveals that he has long been a foreign agent smuggling secrets out of the country. He meets with special branch officer Inspector Brown and offers to reveal the identity of an elusive master spy in return for a reprieve. With five days before Pitt is to be hanged, Brown sets out to trace the identity of the spy without having to offer Pitt a reprieve.