Technically, there was no
de jure "Great Britain" until 1707, but there was a
de facto nation under a single throne from 1603. Once James VI of Scotland succeeded to the English throne as James I, there was little chance the two kingdoms ever going their separate ways again. By 1707 the Scots were almost broke, thanks to the failure of the Darrien expedition, and were quite ready to vote for a Union, in return for access to the English exchequer and guaranteed Westminster representation that is (still) out of proportion to the Scottish population.
Given that the Scots still have separate laws, now have their own Parliament and the "West Lothian" question has never been seriously addressed, you could even argue that the UK has never really come to terms with being one country anyway.
But - and this is the important bit - it added nothing to gameplay to make the British player manage three national budgets (England and Wales, Scotland, Ireland) and separate military establishments. Did you really want to spend your game shuffling money between England and its poorer neighbours and playing, in effect, Total Regional Policy?

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