I'm sure that Mr Beesley, being a very accomplished gunmaker and inventor, had his own design of lockwork made up for him by the Wolverhampton lockmakers. By examining a number of guns we might find a Beesley style of lock.

Most of Beesleys production was best quality. I don't recall seeing a second or third quality by him.

Rocketman, sorry to have overlooked your question. Generally,I have noted higher Whitworth tube numbers on later guns, however, a gunmaker may have tubes dating from the 1880's in stock and not use them until the 1930's; I believe they started numbering the tubes with the introduction of chopper lumps as a way of keeping pairs together. This would account for the absence of numbers on early dovetailed Whitworth barrels.
All the best, Mal