Here are my thoughts!The leigh family of gunmakers are recorded as active in London from 1792-1859. In the past I have encountered breech loading guns made in Belgium For the export market, that are engraved with the name of a defunct London maker.
As suggested,it could also be the name used by an as yet unidentified hardware store or dealer. A similar gun is offered for sale on the internet,in this case it is engraved,"Henry Leigh, Wildfowl gun." The gun illustrated looks like a very good example of the export gun,circa 1880 with above average finish.
