We can positively say it could be made anywhere... The moulds and barrel keys (that's what they called them) and the pistols themselves ( most are generally called Queen Anne or Screw Barrel) were made in large numbers from the early 1700's to about 1870 or so..
I've seen some with the square key like yours, some with actual octagon holes on the end of the handle to fit around the barrel and round holes with a "keyway" to fit on a projection on the barrel... and so on, in a multitude of designs.
the only thing these were for is the barrel screwed off, put the ball in, then powder, then screwed it back together, this was to make a hard hitting little round, that could be carried without fear of the ball coming loose in the barrel and creating a air pocket. and the ball would be swaged when fired and more accurate in a small pistol.
And by the way, there were some guns made in the 15th century with square bores, they were described in a book I once read, the explanation was "round bullets for Christians, Square bullets for Muslims and other savages" this was in a text from the 1400's I believe. It was in a gun history of design and evolution book.