Webley & Scott made a really nice small-frame .38 Revolver, which was also available in .32 and .22 calibres. It went through several Marks, ended up as the Mark IV small-frame revolver, which was the start point for the development of the "Enfield" revolver which was adopted in the 1930s.
The Government decided to concentrate ALL manufacture and repair for everything at Enfield, an impossible situation when they had only one full line and a large shop for shop projects. After Dunkirk, new government finally decided to do something, and Webley & Scott got a contract to build a whole pile of their small-frame .38 revolvers for military/naval/air use. This is the common Mark IV .38/200 of War Two use, taking a .38S&W casing with a 200-grain lead bullet, later superceded by a 178-grain RNFMJ.
W&S automatics were used in the Great War in calibre .455 Auto Mk. II.
They did make a line of pocket automatics, including the Metropolitan model, which are fun to play with and were the inspiration for the H&R pocket automatics of the 1920s. These were available in .32 and 9mm Browning Long (which was actually pretty short). I don;t know about Service use of these but would not be surprised at anything.
Likely I'm 'way off-base on this whole thing, anyway. How about a photo? "You show us yours, we'll show you ours".