Wikipedia gives 1707 ...
"Since the union of 1707, the entire island has been one political unit, firstly as the Kingdom of Great Britain, later as part of the United Kingdom of Great Britain and Ireland, and then as part of the present United Kingdom of Great Britain and Northern Ireland. Since the formation of this unified state, the adjective British has come to refer to things associated with the United Kingdom generally, such as citizenship, and not the island of Great Britain."