Yes, but is it detection? Like
The Face on the Cutting-Room Floor, which appeared at about the same time,
Prelude to a Certain Midnight is a self-indulgent piece of wordplay that has little to do with telling a story or solving a crime. Its main goal appears to be sketching characters; filling in detail about Soho-dwellers of the Thirties and their hangers-on. These are drawn convincingly enough. Their silly names tell us, though, that this is all really a game -- a Noel Coward drama in prose form, full of brittle conversation and very little real emotion.
Kersh seems to have preferred the short story form. I think he should have stuck to it.
Jon.