Here is some information about George Davison from British Gunmakers, Vol 2, by Nigel Brown
GEORGE DAVISON, Market Pl,
Alnwick, Northumberland 1810 & 1826
also at Pilgrim St, Newcastle upon Tyne 1823 & 29
Collingwood St 1826.
Based on the engraving on the butt plate and the leaf pattern around the border of the lock, I would say this piece dates to the earlier part of of his time at Alnwick, in the early to mid 1810's.
What do the proof's look like?
Mike