Getting rid if the Queen?

[Banquo's Ghost]

If the Queen did do that, it was the darkest hour of the Monarchy for a long time.

Monarchy is supposed to block measures that abuse powers, no facilitate them.

Actually, the monarch has very limited powers to block anything without provoking a full-blown constitutional crisis. She is there to give assent, in that power is considered still to derive from the Crown, not the people. But exercise of that power is entirely down to the people's representative Parliament and its executive, which the monarch may not gainsay.

The Queen does not use the Royal Prerogative, the Prime Minister does. He does not have to ask her for permission, but if he does, she has no choice but to give her assent.

The Queen is blameless in any use of the Royal Prerogative.