It was called "The British Empire" from at least 1708, for example in the book by John Oldmixon from that year titled, "The British Empire in America".

http://www.newworldencyclopedia.org/entry/British_Empire

Given that the Act of Union between England and Scotland had only taken place in 1707, creating the Kingdom of Great Britain, this is pretty early.

According to "The Online Etymology Dictionary", from 1772 it could also be called "The Empire" (at least in English), and this would be interpreted as meaning the British Empire. (Before that, if you said, "The Empire" people would assume you were speaking of the Holy Roman Empire.)