Actually, "British" in the sense of the late 16th-early 17th centuries only pertains to the shaky claims of a Protestant Scottish king over his English (, French) and Irish dominions, inherited claims from his Catholic mother and father, after the failure of the Battle of Pinkie to secure Mary, Queen of Scots for Edward VI and for there to be an incorporation of Scotland into England as Leon was into Castile.  "British" in the negative sense that you mingle it with, refers to propaganda of Irish Nationalism, beginning in the wake of the American Revolution and onward until the Troubles.