Probably the William Cox fined for substandard buckles in 1763 -69 period
Goldsmiths Hall Apprentice Book 9, page 2 records the apprenticeship in 1779 of James Baker, son of James Baker to William Cox to be taught the trade of Bucklemaker.This is probably William Cox II, and the father of the apprentice may be the James Baker given by Grimwade as entering a mark as smallworker 19 April 1759 at New Court , Bunhill Row