Elizabeth I or Elizabeth II in Scotland -

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 After the ascension of Queen Elizabeth II in 1952,  discussions were held in Parliament (and elsewhere) on how Elizabeth should be styled in Scotland.  Many Scots considered Elizabeth II to be historically inaccurate as the Act of Union occurred after the reign of England's Elizabeth I.

It was pointed out that other countries in the Commonwealth (none of the countries existed before the Act of Union), were using Elizabeth II, but several Scots MPs, according to the Times, were "asking nothing unconstitutional or revolutionary, but merely that the title for Scotland should be 'Queen Elizabeth,' without any numerals."

Another argued that "it would not be reasonable to argue that the Queen should be styled "Elizabeth the Second of England and the First of Scotland."

In Parliament on April 15, 1953,  Mr. Elliot, who represented a district in Glasgow, asked Prime Minister Churchill, "whether, in advising, the Sovereign to assume the title of Elizabeth II, he took into consideration the desirability of adopting the principle of using whichever number in the English or Scottish lines of Kings and Queens happens to be higher."

The Prime Minister responded: "The decision to assume the title of Elizabeth II was of course taken on the advice of the Accession Council and the form of the proclamation was approved by Her Majesty's Government.
Since the Act of Union the principle to which my right hon. and gallant Friend refers has in fact been followed. Although I am sure neither The Queen nor her advisers could seek to bind their successors in such a matter, I think it would be reasonable and logical to continue to adopt in future whichever numeral in the English or Scottish line was higher. Thus if, for instance, a King Robert or a King James came to the throne he might well be designated by the numeral appropriate to the Scottish succession, thereby emphasizing that our Royal Family traces its descent through the English Royal line from William the Conqueror and beyond, and through the Scottish Royal line from Robert the Bruce and Malcolm Canmore and still further back. Her Majesty's present advisers would for their part find no difficulty in accepting such a principle. From this, it naturally follows that there should not in their view be any difficulty anywhere in acknowledging the Style and Title of Her present Majesty."

In other words,  if the heir to the throne is named James, he would become James VIII, and not James III.

The Act of Union (1707)  is rather clear:  Notice the word FOREVER.

That the Two Kingdoms of Scotland and England shall upon the first day of May next ensuing the date hereof and forever after be United into One Kingdom by the Name of Great Britain And that the Ensigns Armorial of the said United Kingdom be such as Her Majesty shall appoint and the Crosses of St Andrew and St George be conjoined in such manner as Her Majesty shall think fit and used in all Flags Banners Standards and Ensigns both at Sea and Land

http://www.legislation.gov.uk/aosp/1707/7/contents