In monarchies where the monarch has limited power, with the government being mostly democratically elected, can a member of the royal family stand in elections to become a Member of Parliament and then become Prime Minister?
If yes, has it ever happened? If yes, can it be a conflict of interest? Could the Prime Minister try to either give more power to the monarch or take away power? If not, which law (of the concerned country) is relevant here?
The United Kingdom is a constitutional monarchy and parliamentary democracy.
I am looking for answers about the UK, though I would be interested in other democracies (European or elsewhere) matching the given criteria.