It is totally unfair to point finger at Her Majesty. It is clear you have no idea about British law making or how the constitution works, or the rules regarding the Royal Family involvement in politics.
What you are reading about is nothing more than formality and tradition which dates back to when the monarchy relinquished power to Parliament. Laws still have to be formally approved by the Monarch, which is known as Royal Assent, in order to become law, although technically the Monarch could refuse to sign and give Royal Assent, this would cause all kinds of political bedlam and would bring the wrath of parliament down on the monarch which would also be backed by the courts, we would see the Monarchy destroyed.
The Monarchy are not allowed to be political and must not show any kind of political bias towards any parties or the policies they propose, so this Royal Assent is nothing more than a rubber stamp of a legal tradition that is still required, one that has worked well enough for hundreds of years.
One advantage of this arangement is that the Prime Minister is required to give the Monarch a breifing of events and meets in private with Her Majesty regularly. Her Majesty has taken this role very seriously and she is very much aware of everything that is going on which is effecting the country and Commonwealth she rules over, so she is not going to rock the boat by refusing to sign a bill based on her personal feelings or belief.
