You might try posting on doublegunshop.com. Some regulars there have reference books on London Gun makers over at least two centuries. And, most of those natives are friendly. (I've gotten impressive information on Henry and the more famous Eggs through them.)
Harold Blackmore lists 4 gunsmiths named Taylor or Tailor in London during the mid 18th century (1740-1780): Issac, John, Joseph, and William. Issac was active in the 1770's although he was also a hardware supplier and ironmonger. John was active between 1704-1761. Joseph was apprenticed to William Turvey in 1721, which means he was probably active from the late 1720's until mid century. William was apprenticed to George and Edward Turvey in 1748, which means he was probably active in the 1750's - 1780's. It is also possible that the Taylor on the lock was not a London maker but worked in Birmingham. There was a lockmaker, Thomas Taylor, working in Birmingham in the 1770's. There was also Edward Taylor working in Birmingham during that same period. They may have sold guns or parts to the "London" gun trade through agents in the city.
I would like to see the proofs to determine if they are London proofs or Birmingham private proofs as there was an Edward Taylor in Birmingham 1767-1786. There was also Taylor and Co. in London 1770-1780 and that is probably the time frame of this gun in my opinion. The trigger guard is a second pattern acorn finial. The thumbpiece is of a baroque design and the style was on earlier guns but used on into the time frame of this gun. Could be a later lock in it also. There is a Taylor in London c.1800. I believe I would need to see some better pics before I bid it past it's current status.