A rifle proofed at London would not have a BNP (Birmingham) stamp, but rather a conjoined GP (Gunmakers' Proof) with the scimitar and NP for Nitro Proved.
Enfield Lock is only 14 miles from the middle of London.
Looks to be enough of this old girl left to allow for a restoration. These old rifles are very nearly the perfection of the bolt-action rifle. They may not be quite as accurate as some of the modern stuff but they are as reliable as a rock, only very rarely need parts and the barrels generally will outlast the new ones about 3 to 1.
If I owned one like this and was a collector and also liked to hunt, I would fit her out with new wood, very collector-like and all-original.... and hang onto that Bubba'd forestock and butt. Glass-bed that fore-end to the action and barrel you have and you have one FINE rifle for Moose.... which can be put back together as a historical military rifle in about half an hour!
Definitely cheaper than a new Remchester.