Starring Tom Conway
It's suggested here but not explicitly stated that detective Tom "Duke" Martin (Tom Conway) has something of a checkered past, as does his comic relief sidekick, Barney Wilson. Which leads me to believe the producers of this British flick (released there as Barbados Quest) were going for something like a Lone Wolf feel but I could be wrong on that count. The same pair turned up in one other film, Breakaway, which was released in the same year.
Rare stamps and murder are the special of the day this time around. Regardless of what might have happened in his past, Martin is on the side of good here and is called in to sort things out. Before long he finds out that there are a few more copies of a certain rare stamp in circulation than there should be. Needless to say he gets to the bottom of things in a sequence of events that are relatively uninspired. Though I will say that this one managed to hold my attention, which is more than I can say for a lot of movies.
Here's a 1956 review that appeared in the New York Times.