Ohhhhhhh man. So I know that for all intents and purposes, I'm a dog, and you're a dog, so you gotta take my word on this.
In Tal afar (sic), in my dessert years, I came across one of these in an ICDC guard post desk drawer. I was 20 at the time and didn't know anything about anything, but the 249 gunner I was with mentioned, Lawrence of Arabia and the British, and whatnot.
Found alongside it was a Cyrillic inscribed Walther Ppk semi-automatic. I thought fer shure brother mouzone would come to claim it, but no such luck. If I can find a picture, I'll share. Tal afar was like fucking Derry, Maine, I swear. Tunnels and shit under the city. Probably a knight from the first crusade down there.
Haven't seen the episode, but the Webley was in very wide use amongst British forces in WW1, so if it featured, it was very likely an intentional nod to the history of the weapon. Or the weapon of the history, whichever you prefer.