Far as I can determine, no gunmaker grew his own trees for stocks, mined his own iron ore for steel, or smelted steel for himself. While it is entirely possible to do small part forging by hand, per Chuck, I doubt that it was done other than for Master training. It makes no economic sense to do in-house forging when out-house specialists are available who can do it probably better and certainly cheaper. The raw action forging doesn't have a big impact on final quality unless it is actually defective and the Brit skill in forging had long passed the point where trade made defective action forgings were likely.
Keep in mind that there was a trade willing and able to supply parts at any state of finish - raw forgings to finished guns. Locks and semi-finished barrels were often bought in, too. For any given shop at any given time, it depended on who was employed in-house and what the order books looked like. Per the success of William Evans, it was far more important that the shop owner enforce high standards for quality and service rather than make guns.
Further, note that the steel used in most gun parts was plain low carbon; springs, for example, excepted. It was easy to work and sufficiently strong for the pressures encountered. When case hardened, it was also quite wear resistant and relatively resistant to corrosion. There were basically no propriatary alloys - steel was steel. The skill lay in close fit of parts all the way through the mechanism and in finish. BTW, IMO, the skill of styling is no small part of high quality work.
