Yes, it can be used in place of a target gripped MK III in an appropriate portrayal. This would be after 1896, probably as civilian of the Empire, as I believe an officers weapon would have to be of the issue caliber, IE .455. I suppose an enlisted infantryman might have one in his kit, much like US troops overseas often carried small revolvers as last ditch weapons. Though perhaps her Majesty's army frowned upon such things? Jack?
I could see US troops possibly acquiring these, as the various Webleys and other small British revolvers were quite popular in the States, and of course the .38 S&W was a very popular round on this side of the Atlantic. The Webley would be on the expensive end of the scale, far outnumbered by the various "Bulldogs" and US made 5 shooters.
Though anyone using one had better have quite a good backstory as to how he got it and why.