We could start by noting that the gun in question is a center-fire cartridge gun that breaks open. Neither of the original Manton brothers, Joseph or John, built such guns.
There were lots of guns produced, mostly at lower price-points, marked J. Manton. Personally, I am not convinced that such guns were so-marked to convince a nineteenth-century buyer that he was getting "best" London gun for a few pounds. It could just as likely be along the lines of Pontiac naming their cars "Le Mans" and "Grand Prix". Free marketing ride, sure, but nobody buying a Le Mans seriously thought it was a race car. GM didn't even have a race program.