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Sir Alex Douglas-Home being the last example of this - he was Earl of Home and Foreign Secretary under Harold McMillan. When McMillan resigned there was an opaque process to choose the next Conservative Party leader and Douglas-Home was selected. He was in the House of Lords at the time. So he could do his job properly he resigned his peerage, and then a by-election was engineered for him to win so he could become an MP. So for a short time he was Prime Minister in the House of Lords, then not in Parliament at all until he won his by-election.

But if I understand Labour Party rules correctly, to be leader of the party you have to be a Member of Parliament. And the leader of the party that has the most seats in parliament tends to become Prime Minister.