The Queen is the commander in chief. She can do anything she wants. She's still ultimately the Sovereign, not the body of the people represented in parliament.
That's the problem. The UK's Constitution is uncodified and is just based on tradition. Suppose her successor (don't know who it will be) doesn't like democracy?
The same problem exists, although to a lesser degree with the U.S. Federal Constitution in that it's written, but it also is ambiguous.
Well, the UK does not have a commander in chief as such, not in the sense that the US does anyway.
For instance, who has the ultimate power in the UK to order the country to war? The Prime Minister does. And right now, without reference to Parliament or the Queen.
Who holds the power to order a nuclear launch? The Prime Minister does, not the Queen.
But you're certainly right, to a degree, about the UK constitution being uncodified .... but to to an degree. It is partially codified, if that doesn't seem like a contradiction in terms. Let me put it this way. Over the years, and indeed centuries, the power of the Crown has been limited and restriced in many ways. Some are formal, written and Acts of Parliament, and some are common law. You can look on common law as "tradition" but it is a tradition that has the force of law behind it because it's been the way some things have been done for so long that courts uphold it.
So sure, the Queen is the monarch, and
in theory has extensive powers, but as I said, she has many of those powers because she carefully chooses to not try to exercise them. For instance, the final stage of the legislative process is the Royal Assent by which the monarch 'approves' any Act of Parliament into law, and in theory, could either withhold or defer assent.
Butr when did the British Monarch last withhold that Royal Aasent, and frustrate the will of Parliament? To the best of my ability to find out, it was 1708. So given about 300 years of not exercising it, I think it's pretty safe to refer to the "power" as largely theoretical, and it's a safe bet that if it ever was exercised, it would rapidly follow that the power would be removed, and quite possibly, the monarchy with it.
The Queen is also still currently Head of State in many (if not all ) commonwealth countries, including Australia and, IIRC, Canada. The same "theoretical" principle applies there. In Australia, laws still require the Royal Assent, given in practice by the approval of the Governor-General. Up until, what, 80 years ago the Governor-General was the choice of the UK soverign, for which you can read UK government, acting on the "advice" of the Australian premier. But that came to a head then the British Government wanted a different G-G to the Australians, and the Australians won that show-down. It is now "tradition" that the Governor-General, while nominally a representative of the British monarch with theoretical powers to frustrate Austrialian legislation by withholding Royal Assent, is actually the choice of an effectively appointee of the Australian minnisters and acts on Advice of Australian ministers. It is, in practice, an entirely ceremonial "approval". And last time I saw a poll among Australians, retaining the Queen as Head of State was the popular choice among a significant majority, but I'd bet by house that that approval would vanish ion a heartbeat if either the British government or British Monarch tried to actually tell the Aussie government what to do, or to refuse to "assent" legislation they'd passed.
While that power exists in theory, if it was ever exercised, it'd rapidly been removed, and the notion of either the Australians or Canadians accepting actual rule, or diktat, from Britain is laughable, even if theoretically and perhaps constitutionally, it may still be the case. And it's much the same in Britain. If no monarch has exercised a power in more than 300 years, it's a safe bet they know what would happen if they did.
So the Queen can do "what she wants"? No, though in theory she has very broad powers, they are ceremonial in practice, in almost all cases. She is the 'ultimate authority' in theory, and when the PM issues orders for defence of the realm, he does so in the Queen's name, effectively including a nuclear launch. For instance, if the PM lost his mind and ordered a nuclear strike, or to go to war, it has been made quite clear by previous heads of the defence staff that the order would not be carried out, and that the option to revert back to the Queen exists. But if that order was legitimate and bucked the will not only of the PM but of the government, and the monarch blocked it, I have no doubt it would spell the end of the monarch's ability to do it, just as withholding Royal Assent in Australia would result in the removal of the monarch.
The "tradition" that things are done a certain way is, in fact, a very powerful driver, and while it may not have the codification that the US constitution has, it is ion some ways, more rigid and powerful even than that. For instance, it's far from unknown for lawyers to try to either change the constitution, or to find exceptions, reinterpretations or loopholes, while with much of that "tradition", it hold so strong largely because much of it is not written down, and smart-ass lawyers can't try to weasel reinterpretations out of if in the same way.