The Queen does in theory hold the right to dissolve Parliament and as head of the armed forces does in theory have the ability to back it up...However as far as I can see she (and her recent predecessors) have had no call to do so..The right conditions have not been pertaining to such an action.
Whatever we may think of the policies of recent governments, none of them have been really undemocratic even when we had such close hung Parliamentary votes under Major.However if we ever get a truly hung Parliament I'm sure the Monarch will act to sort matters out by inviting whomever gets the agreement of other parties to make up the government or to go back to the electorate to get a majority.
So in fact she does have power but doesn't see any need to use it leaving it to common sense on our part as a democracy to exercise that democracy.
