The uk and us are definitely referred to as nation states in cyber Warfare lingo. I think the meaning is close to: group with lots of resources and strategic goal directed in that context.
A nation state is a nation that is also a state. The UK clearly is a union of four nations into one kingdom. I mean - the clue's in the name.
Additionally "nation" can refer to the collective people rather than a centralized government in action.
Unless you're going to separate out historic county kingdoms (Wessex, Sussex, Kent, Gwent, etc.) then England annexed the counties that compromise the region we now call Wales as lands of the English Crown.
The UK was initially formed by the Union of two kingdoms, England and Scotland at which time all the parts of Great Britain were under the same Monarch.
Your contention doesn't necessarily disagree with this historical fact.
It's "the United Kingdom of Great Britain and Northern Ireland", not the "United Kingdoms of Great Britain, Northern Ireland, and whatever 3rd one you have in mind"
I was under the seemingly false impression that the Queen was separately Queen of England and Scotland still/again. But it does appear she is Queen "of Great Britain, Ireland and the British Dominions beyond the Seas" making her Queen of 2 kingdoms (Great Britain, Ulster) within the UK?