Okay gonna stick my neck out on this one, as I don't have any history books at hand; but as I recall ...
the idea of "Great Britain" and the Union flag arose out of the ascension of James I and VI to the throne of England; and the subsequent great excitement (especially in Whitehall) with the idea of a united monarchy over all of the British Isles.

...but I'm sure someone else will correct me on that.