Is there a scenario in the last century where a political party in the UK could have won enough seats to form a government, but had its leader - be they an incumbent Prime Minister or not - lose his/her own seat? If so, who would have been a likely replacement as Prime Minister?
Indeed it was only recently that members of cabinet did not have to resign their seats to be members of the cabinet...
AFAIK this is utterly wrong. Ministers are required to be MPs or Lords, and an MP cannot legally resign.