I am not an expert in revolvers and handguns but I have had to handle a Webley long enough to wonder how can you tell on these parts that it's from a Smith and Wesson and not from a Webley.
The Webley was the standard issue service pistol for the armed forces of the United Kingdom, the British Empire, and the Commonwealth from 1887 until 1963, so frequency argument is in favor of the Webley. The Webley Mk IV .38/200 was the standard post 1914 issue, externally almost identical to the Webley .455 ww1 issue.
The second most frequent revolver in the UK in ww2 was the RSAF Enfield No. 2....which was a copy of the .38 Webley!!!! (the whole legal story of the development and production RSAF enfield is a crazy one - totally impossible nowadays).
If the parts were collected in the UK, all the probability is towards one of these 2 models, not the Smith and Wesson, an US made model, that, to the best of my knowledge was never a British Army issue.