I wish Justin Trudeau was Trump....
Popular vote is not necessarily a good thing (Looking at you Boaty McBoatface and those who made it possible)
Britain is a Democratic Monarchy, much the same as Canada, they still have elections, Ministers are the same as the Presidential Cabinet, all appointed, in a Democratic Monarchy, it simply requires the queen to sign off on it ((essentially) in reality this normally falls to the Governor General (Queens Rep)
I'll avoid france, since I'm not quite as familiar, though it is a Republic from what I recall, and it's Democracy is based off the American system.
London has a mayor.
Paris has a mayor.
Brexit is a perfect example of Democracy in action, and why the popular vote is not always correct, which is why almost all modern democracies, (unlike the ancient greeks) use some sort of representational democracy.
Frankly, Aristo, take your time, I'm having fun :D