I have a Webley Mark IV 38 with a cross bolt safety. Plenty online about Webleys and nothing about the safety. I'm sure this model is a civilian model due to the lack of any lanyard
ring and police or military markings.
Neat gun, I've never seen the compact model in person. There were some of the safety revolvers imported a while back (yours looks like the Webley Mk IV Pocket Double Action Revolver), some were marked HKP or XXX'd out on the butt, some weren't. Typical funky weird British engineering, IIRC, it was to make them drop safe by locking the trigger and hammer. I'm not sure who makes .38/200 cartridges anymore, most .38S&W is around 145gr now. They're not known for being particularly robust so keep loads on the mild side if you decide to reload for it. One of my uncle's likes Enfields and has or had (don't know if he still does) a couple of Enfield and Webley revolvers as well as a British S&W Victory in .38. I've shot his .455, never shot one of the .38s.