Well, I can't say as I remember my history lessons all that well, truth be told. But if I recall, it wasn't a war that did it - Scotland's king inherited the English throne. After Good Queen Bess, I think it was.

And then, well, it made sense to keep the same laws in both countries, so the Scots agreed to join and become Great Britain.

[Also Scotland was broke as fuck, and England was afraid Scotland would side with Spain against them.]