DiogenesLamp: "Your point is wrong.
This makes it a non point.
"Union of the Crowns." 1603.
"Acts of Union." 1707. "
jdsteel is correct, the term "United Kingdom" was created in 1801.
Before 1801 other terms were used, especially from 1707 on:
According to the Encyclopedia Britanica:
"The term "British Empire" was frequently used after 1685; for example, in John Oldmixon's book The British Empire in America, Containing the History of the Discovery, Settlement, Progress and Present State of All the British Colonies, on the Continent and Islands of America (London, 1708).[1]"
Further, there was nothing ever voluntary about "British union" -- kingdoms were forced into it and left only by rebellion.
It was, in short, a typical empire as that term is understood from time immemorial.
By stark contrast, the American Union -- which George Washington himself called "our empire" -- was of a very different nature, more analogous to the original ancient Greek Delian League:
Still a Union.
United into One Kingdom by the Name of Great Britain