In English-language discussion, the British colonies that became the USA were sometimes called the "American colonies" (or "North American colonies"). Examples:

• The Justice and Necessity of Taxing the American Colonies Demonstrated (London, 1766)
• The Grievances of the American Colonies Candidly Examined (London and Providence, 1766)
• Memorial on the General Culture of Lands in Our American Colonies (Edinburgh, 1766)

Of course, Britain had many colonies on the American continent other than the thirteen who became the United States: this list from 1774 includes Hudson's Bay, Labrador, Newfoundland, "Canada" (i.e. Quebec), Nova Scotia, and East and West Florida -- not to mention the Caribbean islands such as Jamaica and Barbados. However, I'm not aware of any usage of the phrase "Thirteen Colonies" until after the revolution.