In this country we don't vote for the PM but rather the political party. At the last General Election, Tony Blair was the leader of the Majority party and as such, Queen Elizabeth invited him to form her Government. Labour's leadership changed and The Queen then invited the new leader to form her Government. The same thing happened when John Major replaced Thatcher as Tory leader.
technically we don't even vote for the party but for the individual candidate in our constituency. Of course some people will vote for a monkey if it's in the party they favour