There is a lot of misunderstanding surrounding both how a PM is elected and also how a general election is called.
First of all a PM is ascended to power through his or hers party winning a majority in a general election or being able form a stable coalition. The British electorate elect local members of parliament not a prime minister. A party leader who is able to form a stable government then is given royal ascent by the Queen to become Prime Minister.
In the event that the PM then leaves their post through death (Perceval), choice (Blair) or is forced out (Thatcher) then there will be an internal party election for a new leader. Anyone can join to become a member of a political party to take part in this internal election.
Secondly because of the Fixed-term Parliaments Act 2011 only a vote of no confidence in the Government (by MPs) or two third majority of MPs deciding there should be a general election will actually result in a general election. A demand by a small percentage of the population for a GE will not come to fruition.