British North America
British North America was what the British-owned part of the continent of North America was called, mostly before the American Revolution. See History of the United States#Colonial America. After the Battle of the Plains of Abraham the colony of New France was also under British control.
After the American Revolution, some people still used the term to refer to what is now the country of Canada, and in fact the Canadian Constitution was first called the "British North America Act 1867" (that being the year in which it first became a law).