The 20 Questions Murder Mystery (1950)
I really enjoyed this as it weaved a mysterious whodunit murder mystery, where somebody was knocking people off using the Thuggee method of strangulation with a silk cord.
Robert Beatty, the Canadian "Yank" who was in many a British film played the lead role and there were a number of recognisable faces, including Mr Quelch (Kynaston Reeves), and there was Wally Patch again as the heavy and according to the IMDb June Whitfield had an uncredited part with no character name and I have to confess I didn't notice her.
Based around the very popular BBC radio series "Twenty Questions" it had a number of people playing themselves including Richard Dimbleby.
Oh, and a suspect was Mohammed Ali.