I don't have a WW2 'other ranks' cap badge to show you but I do have a pair of officers collars - exact same design as the cap badges, but these officer badges are in what is called 'OSD' finish that's 'officers service dress' - it's an applied colour to give a patinated bronze appearance, in fact many just call these 'officers' bronze'.
The men in WW2 would wear this badge in brass.
This Fleur-de-lys design was worn from 1923 to 1958. It was completely different from what they wore in the Great War.