My Nigel Brown books on British gun makers do not list W&G Chance of Birmingham. This means they were most likely a small trade shop. They were by no means on par with Manton, Mortimer, or Twigg.
At the time the Chance rifle was made (ca 1810-1816) the London gun trade was supreme. The Birmingham makers were wholesale parts suppliers in general, with a few firms turning out completed guns. Most of the Birmingham trade supported the Government or export market. There were some Birmingham firms turning out complete guns for retail, but in general, the fashionable went to London to get their guns, and turned their noses up at a Birmingham produced gun. That is not to say that Birmingham makers were not capable of really good work, but it wasn't until about 50 years later that the Birmingham firms came to be on par with the London quality guns. Even then, the bigger Birmingham firms like Hollis, Webley, or Richards, had shops in London, and had their top class guns proofed in London, so they looked "London" built.
John Manton is considered by some to be the premier English gunmaker. His only rivals for that title would be H. W. Mortimer, and John Twigg, who John Manton learned the trade from, and perhaps Joe Manton, John's younger brother.
The flintlock rifle I have by Perry was made by a similar small Birmingham firm between 1806 and 1812. It has a top notch lock and Siddons single set trigger which is the same supplier that provided the single set used on the Chance rifle. The fit and finish of this rifle is as fine as some of the London made flintlocks by top name makers like Baker and Smith I have from the same period.
Another interesting twist to the tale of English flintlocks in America are the Indian trade guns the British Ordnance purchased and gave to various nations they were trying to negotiate/deal with. These have fore-end /ramrod entry pipes that are much more American styled than the typical English type.
Mike