Proof? OK ... Let's start with a speech from the Prime Minister in 2020:
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https://www.gov.uk/government/speeches/prime-minister-opening-statement-second-reading-of-the-ukim-bill
The creation of our United Kingdom that has stood for centuries by the Acts of Union of 1707 and 1801 was not simply a political event but an act of conscious economic integration that laid the foundations of the world’s first industrial revolution and the prosperity we enjoy today.
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This shows that, according to the Prime Minister at least, the creation of the United Kingdom comes from the Acts of Union of 1707 and 1801.
The 1801 reference is the Irish part, which we can leave out here. The Acts of Union in 1707 were two Acts of Parliament: the Union with Scotland Act 1706 passed by the Parliament of England, and the Union with England Act passed in 1707 by the Parliament of Scotland. They put into effect the terms of the Treaty of Union that had been agreed on 22 July 1706, following negotiation between commissioners representing the parliaments of the two countries. By the two Acts, the Kingdom of England and the Kingdom of Scotland — which at the time were separate states with separate legislatures, but with the same monarch — were, in the words of the Treaty, "United into One Kingdom by the Name of Great Britain".
Some Government links among many others confirming this:
http://www.nationalarchives.gov.uk/pathways/citizenship/rise_parliament/transcripts/articles_union.htm
https://www.legislation.gov.uk/aep/Ann/6/11
https://www.legislation.gov.uk/aosp/1707/7/data.xht?view=snippet&wrap=true
https://www.nrscotland.gov.uk/research/image-gallery/doors-open-day/the-articles-of-union