Barbados Quest (1955)

J. D. Everleigh, a wealthy American, purchases a rare stamp in London from Geoffrey Blake, who says he represents Robert Coburn, a stamp agent. Everleigh begins to suspect the stamp is a counterfeit and hires private-detective Tom Martin to investigate. In London, Martin, assisted by Barney Wilson, a reformed crook, learns that the real stamp is still in the hands of Lady Hawksley but she refuses to show it to him. Martin gets friendly with Lady Hawksley's secretary, Jean Larson, and learns that Blake is a neer-do-well nephew of Lady Hawksley. Murder also rears its ugly head as Martin finds clues that seem to indicate that everybody he encounters is involved in one way or another with stamp counterfeiting.

https://www.imdb.com/title/tt0049525