I'm a bit late to this thread, and unfortunately my pinfire Reilly carries no particular patent information. But I do have three guns with patent use numbers:

12-bore double-barrelled bar-in-wood pinfire sporting gun by John Blissett of London, serial number 4067, made @1863?, with J. V. Needham patent side-lever fastener (rotating bolt single bite snap action, self half-opening, patent 1544 of 1862), patent use number 171 (see the silver poincon).




12-bore double-barrelled self-half-cocking underlever pinfire sporting gun by Cogswell & Harrison of London, serial number 5904, made 1864-1865, push-forward underlever single-bite snap-action with half-cocking feature (Edward Harrisons patent No. 271 of 1864), patent use number 26 (you can see the number engraved within a cartouche on the action bar).



14-bore double-barrelled pinfire sporting gun by the Masu Brothers of London, serial number 2309, made @1865-69, with Bastin patent underlever action with a forward-pivoted pull-down underlever with hinged catch (patent 2395 of 1856), patent use number 598 (stamped on the underlever, but not visible in this photo).



I don't know if the Needham action was supplied to Blissett in the white already numbered, or if he made it and added the number, or if Needham made the whole gun and Blissett added his name. The gun is London proofed, so if Needham made the gun, wouldn't it be more likely for the gun to carry Birmingham marks? In this case, I would presume the action was obtained in the white, and barrelled and finished by Blissett.

The Cogswell & Harrison gun uses their own patent, yet there is a patent use number. I don't suppose they pay themselves a royalty (?), so numbering their guns in this way is just for marketing? The matter is confusing. In any case, the 26th gun is pretty early in the patent's use.

The Masu gun has the numbered Bastin action, but the gun carries Liege proofs, and one of the Masu brothers continued the business in Belgium, while the other, Gustavus, operated the London operation. It would seem that the barrelled action was Belgian sourced, and either the gun was completed in Liege and sold in London, or the barrelled action was brought to London for finishing.

I believe William Powell & Son lifter-action guns (Powell's patent no. 1163 of 1864) carry a patent use number, but unfortunately mine (a 12-bore bar-in-wood number 3790 first made in 1866 as number 3690 and re-numbered and re-sold by Powell in 1869) was converted into dual-fire and the modification to the action bar to allow an extractor obliterated the patent use number.

I hope others will add to this threat. The whole matter of patent use numbers and what exactly they signify in the process of building guns is a mystery to me.