So the UK is run by pedophiles.

This is a bit of a misstep right out of the gate since the UK is considered a constitutional monarchy. Though it's generally considered a formality today, technically, in order for any bill to become an act of parliament, it's required to get royal assent. Which is the monarch's approval. And literally, stories have come out recently of the monarchs themselves changing legislation using their influence. This, actually, like the royal assent not being granted to a bill, hasn't happened since the 1700s. And if it did today, it would almost certainly prompt a crisis. Yeah. But in terms of the law and how the government is organized in the UK, the monarch has the power to override everything that any elected body does. The UK is not a republic by any stretch of the word.