A theoretical question about politics!?

Question

If the Prime Minister (not just Gordon Brown, but any Prime Minister) were to hold a by-election in their own constituency and lost their seat, would they still be Prime Minister?

Answer 1

The Prime Minister is normally whoever the Queen chooses to lead a government.  To be effective, it has to be someone whose policies can command a majority in the House of Commons, but the Prime Minister does not necessarily have to be a member.  

Alec Douglas-Home became Prime Minister when he was a member of the House of Lords.  He renounced his peerage and stood in the next parliamentary by-election. He lost.  One of his party then resigned a safe seat and smart Alec eventually managed to secure a seat in the Commons, but he was Prime Minister for a few months before he got there.