There was no general election when Gordon Brown took over from Tony Blair.
I know that, in theory at least, people vote for the party, not the leader. The Blair-Brown transition wasn't unprecedented, but equally morally and ethically questionable. The difference here is that the Tories, who currently have a significant majority, are in complete disarray and are clinging to power that, if the latest polls are to be believed, would see them all but wiped out.
It's extremely common in British politics for the prime minister to change without calling a general election. In fact there were only two PMs in the entire 20th century (Heath and Attlee) who both entered and left the premiership as the result of an election.
Anyone who complains about "unelected PMs" needs to read more history.