To say they have not been elected is a complete falsification of our parliamentary system. The UK general populace has never voted for a PM. Party members do, and every single prime minister (bar some few exceptions) have been elected by their Party in some way, shape, or form. The four PMs you mention were voted into power by Conservative voters. Conservative members decide who to lead their party, not the anyone else. This is why you don't get situations like you do in the US, where the President can be of a different party to most of those in government (and little ever gets done because legislation gets caught in either house or senate as a result).
We vote for MPs, not Parties. The PM could lose their seat if their local constituency votes them out, even if every other person in the country voted for them. An example of that is the 1906 election [1], where Balfour lost his local vote and the Conservatives had to scramble to come up with a new leader. This is why top MPs are given safe seats by their respective parties. Of course, in practice, the vast majority of people vote for their Party not their local MP when they go to the polls during a general election. That isn't how the system is designed to function though. Most people couldn't even name their local MP - the one who is actually meant to represent their personal interests - which is an utter travesty and the source of most of this countries political woes.
We vote for MPs, not Parties. The PM could lose their seat if their local constituency votes them out, even if every other person in the country voted for them. An example of that is the 1906 election [1], where Balfour lost his local vote and the Conservatives had to scramble to come up with a new leader. This is why top MPs are given safe seats by their respective parties. Of course, in practice, the vast majority of people vote for their Party not their local MP when they go to the polls during a general election. That isn't how the system is designed to function though. Most people couldn't even name their local MP - the one who is actually meant to represent their personal interests - which is an utter travesty and the source of most of this countries political woes.
[1] https://en.wikipedia.org/wiki/1906_United_Kingdom_general_el...