Actually the King/Queen can reject a PM and if they really wanted too they could dissolve Parliment which does put a check and balance on the Commons and the PM.
The King/Queen is apart from the powers above just the cerimonial head of state - the PM holds most of the power and last time i checked we do elect them so saying we are not "democratic" is somewhat a leap.
The Monarchs powers are layed out in a number of documents and barring millitary coup they wouldnt be able to gain anymore without the commons support.
What we REALLY need in the UK is a single written Consitution defining the Monarchs and the Houses roles and the rights of the people as we currently are stuck with an emalguration of numerous court rullings/treaties.
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