The Queen is the 'Head of State' which, ever since there's been a parliament, means that she's not so much the owner or even manager of the UK as a figurehead of the UK. She does own royal estates and land but, in practice, she doesn't really own the rest of the land other than in a symbolic sense.
If our modern Royal Family were despots then there'd probably be a fuss but no major political parties have meaningfully expressed a desire for the monarchy to be disbanded.
They don't cost much per person in the UK per year and they undoubtedly will help tourism too. They probably make the UK more money, and supply more emotional and inspirational benefit, than they cost.
If a prime minister went absolutely mad and yet his own party backed him and an ineffective or complicit opposition didn't oppose him, then the existence of a benevolent monarchy might be very useful indeed too. In fact, her example might have repercussions within how parliament itself conducts itself. Without our particular rather benevolent monarchy, our elected parliament itself might become less benevolent.
So, in a strange way, having a benevolent monarchy might make us a more truly socialistic country in a cultural sense (where we care for our neighbours, our community, we care for industries that actually make more than just money as a meaningful part of existence), if not a political one.