Who were the major players in Birmingham who supplied trade guns to other makers for rebranding? Is there anyway to tell who made what for the trade guns, any tell tale signs or nuances to reveal the maker?
What period are you interested in? Before the 1870s and the wider use of steam powered machinery, parts and/or whole guns were hand-made and supplied by hundreds of small operations and individual outworkers, mostly operating in Birminghams gunmaking quarter. Several makers there became quite large operations, with hundreds of workers operating more and more machinery. By the end of the century several large firms supplied a great many guns to be re-branded. However, my knowledge gets spotty after 1870, so someone else will have to chime in.
In some cases the inside of locks, actions, and barrels may be signed or have makers marks that can identify firms or individual craftsmen. Some makers record books, if they have survived, identify the individuals that supplied various parts. Do you have a specific gun in mind that you are trying to trace?