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This pistol is indeed curious overall & doesn't conform to any British Military pattern that I know of or can find listed etc.

The pictures aren't really clear enough to tell if it is all genuine/original etc and one striking feature is - as you point out - its rear sight. This sight is more like that found on a smooth bore P 1858 musket for Indian service. Percussion pistols typically had either a two leaf rear sight, on 10 inch rifled pistols for example, and some 6" SB pistols had a simple rear sight on the very end of the breech. Most smooth bore pistols had no rear sight.

The other equally odd feature is the distance between the end of the barrel & the end of the stock, nearly double what is "normal". The extra length is from the swivel bracket lug to the muzzle, this lug is about the correct distance from the stock but is usually fixed very close to the muzzle end to allow the rod to get into the bore. Unless the swivel arrangement on this pistol has an extra part over the "normal" set up (if so its not visible in the picture) it is assembled "back to front" &, in theory, won't work either the way it is fitted nor even if fitted as per "normal".

The date is also odd, again as you've also pointed out, the hammer is a little too straight & "chunky" for an earlier pistol, more like a later production P/53 hammer, & this seems to be in keeping with the lock date.

If you can please inspect the barrel & provide length & bore details & post some close images of the swivel arrangement and lock & the other side etc may be able to comment further.
A. Roads