Birmingham-ish proof on barrel. Which might mean it was made there. Also can mean it was a gun from one of the assorted contracts the Brits had with Continental makers, the so-called "Belgian" contracts. These imported guns were proved (and occasionally re-proved) in Birmingham. I have one such "Belgian" musket, actually I think it was made in Denmark, with both original Dane proof well worn off + Birmingham proof & view marks.
With respect to that cut-down Brown Bess story, consider measuring the barrel diameter about at the touchhole. Muskets were much larger here than were pistols of similar caliber. I have an .80 cal plain flint pistol, possibly early British sea service, single bridle lock. The barrel measures 1.195" across at this point, same as my .65 cal light Dragoon . My India pattern Brown Bess musket is 1.334. Both measured about 3/8" ahead of breech, with Vernier calipers.
Minor point, might be nice to see the front end of that trigger guard finial, also fairly close view of the thimbles. Don't claim to be expert here, but it seems to me that pistols for the sea service tended to be simpler than for land service, maybe not so picky about precise patterns. Your sideplate is British.