According to Walter Bagehot's, the English Constitution the monarch has three main powers:
- the right to be consulted;
- the right to warn;
- the right to advise.
He or she also has the right to dismiss the Prime Minister if the Prime Minister no longer has the confidence of the parliament.
Bagehot's view was the British monarch would have to sign his or her death warrant if parliament were to pass legislation authorising it.
Effectively, that's true, but legally, I don't know of anything in writing that says the Queen can't withhold Royal Assent from a bill. If she tried for any reason other than the PM going insane the UK would become a republic extremely quickly (How exactly you get royal assent for the bill that abolishes the monarchy, I'm not sure, it would probably require a weapon of some sort...).