Xjyuk

A couple of days ago, the UK Supreme Court ruled that Boris Johnson's advice to the Queen, which led to the prorogation of Parliament for 5 weeks ahead of the October 31st Brexit date, was unlawful. Therefore, the prorogation has been cancelled and Parliament has been recalled.

However, my understanding (which may be incorrect) is that the act of proroguing Parliament is a royal prerogative power of the monarch. Although, they are supposed to take guidance on the matter from their Government.

So, does that mean, at least in theory, that the Queen could overrule the Supreme Court's decision to cancel the prorogation, by citing her royal prerogative. Essentially: "Yes, the advice given to me may have been unlawful, but I still want Parliament prorogued anyway."

No.

I suggest the best source for this is probably the ruling of the Supreme Court itself. I'd encourage you to read it in full - it's not long and surprisingly readable.

The legal argument the Court made starts by establishing that courts have the right to limit the use of the Royal Prerogative (for example, see paragraph 32). It further establishes that such limits also apply to prorogation (see, for example, paragraphs 41-44). It then moves on to discuss where exactly the limit on the power of prorogation is, finding in Paragraph 50 that:

a decision to prorogue Parliament (or to advise the monarch to prorogue Parliament) will be unlawful if the prorogation has the effect of frustrating or preventing, without reasonable justification, the ability of Parliament to carry out its constitutional functions as a legislature and as the body responsible for the supervision of the executive. In such a situation, the court will intervene if the effect is sufficiently serious to justify such an exceptional course.

The Queen is as bound by this as the Prime Minister.

(In case of any doubt, note that I am not a lawyer. I probably don't need to say that, but I feel better saying it just in case.)

When you start to consider the way the UK consitution works you need to distingish clearly "The Queen" (a 93 year old woman who like horses and Corgi dogs) from "The Queen" (Dei Gratis Monarch of the UK, embodiment of the power of the State). As the spelling is the same, it is easy to become confused, but The Queen is not the same as The Queen.

The Queen (The woman who likes horses) doesn't wield any actual political power. She does get to have meetings with the Prime Minister, and will offer her advice and wisdom. She certainly has influence, but she can't just decide to prorogue Parliment and so on.

The Queen (The living embodiment of the State) can prorogue parliament, but this power is exercised purely on the recommendation of the legal advice of her ministers. There is a fiction in the UK constitution that the Queen makes certain instructions, such as proroguing Parliament. This is a legal fiction, as The Queen (Monarch dei gratis) can only ever act on advice.

So the Queen can't in theory say "Actually I want to prorogue Parliament". It is not within her personal remit do so. It would be "interesting" if the Queen did decide to take political decisions without ministerial advice. But as with any unconstituional action, the constitutional effect would be unpredicatable. She could well be told to abidcate, or have such reserve powers removed from her.

In the UK constitutional system, the Queen is not above the judiciary—she is the judiciary. As Wikipedia notes:

The sovereign is deemed the "fount of justice"; although the sovereign does not personally rule in judicial cases, judicial functions are performed in his or her name. For instance, prosecutions are brought on the monarch's behalf, and courts derive their authority from the Crown.

Thus, according to the constitutional principle she exercised judgement, it was ultimately her decision (a decision in her name). It doesn’t make sense for her to redecide without any new evidence being presented.