I used to work as a scholar of Britain (specifically executions in Early Modern England, but you pick up a lot along the way) and I've tried to explain to a lot of people the amount of influence and control that the monarch actually holds. I'm not sure that this is such a bad thing. The Queen can't create legislation, she can restrain it. She is purely a moderating influence in this sense. She could, in theory, name new people to the House of Lords, but the Lords is no longer a hereditary body and there is a mechanism for the House of Commons to override the Lords.
Parliament does have power over the monarch in some senses, of course, in that there is precedent for Parliament changing the order of succession or introducing a regency. This happened without the monarch's assent, though admittedly over a hundred years ago. But the British constitution is one that replies on precedence, not a formal document.
I've characterized the Queen's powers as "reserve powers" inasmuch as, if everything goes wrong and Parliament dies from a meteor strike, the government still legally operate provided there is a monarch (even if you have to reach deep into the line of succession to find that person). By law she has to call elections within a certain amount of time. Obviously there's nothing to force her to follow the laws, but that's true of any country. She (or her heirs) are the leaders of last resort.