Nothing in my cup at the moment. I must get some iced water shortly.
The UK Monarchy is an oddity. Rule is by custom, rather than by written constitution. The armed forces
swear personal allegiance to the current monarch, and their heirs and successors.
The UK monarch must assent to any laws passed by the Houses of Parliament, although this is now a formality, and Royal Assent has not been refused since 1707.
Parliament rules, but the Queen does have a weekly meeting with the Prime Minister, and no doubt has influence behind the scenes. In public, the monarch remains strictly neutral with regard to party politics.
I was fascinated to read about the Belgian Monarchy, which is a much more constitutional monarchy than the UK one.