Qfyilyi

This question as quite hypothetical as I don't believe it will come to pass, but…

There is an ongoing situation in which Theresa May, Leader of the United Kingdom Conservative Party and Prime Minister of the United Kingdom of Great Britain and Northern Ireland, is facing a leadership challenge. If she loses, she cannot take part in the subsequent leadership election.

It has been said that currently, the Prime Minister faces a rather impossible job. I can imagine many good reasons to not want the job. In theory, if there is a leadership election but no candidates (or no candidates with enough support to get their name on the ballot), what happens next? Will the position remain vacant?

Conservative party rules require that the Leader is an MP. The constitution only requires that "There shall be a Leader of the Party, drawn from the Members of Parliament" It doesn't give any remedy in case no MP is willing to stand. It would be a big problem for the party, but no laws would be broken. The existing Leadership would probably remain in a caretaker role until someone is willing to stand.

In terms of the constitution, the Prime Minister and Cabinet must nominate their successor. Normally this would be either the next leader of her party, or the leader of the opposition (in case that she had lost a vote of confidence and the leader of the opposition had been able to form a coalition).

In the exceptional circumstances of there being nobody willing and able to form a government then surely MPs would have no confidence in the government, and a new election would be held. These would not be business as normal, and would probably lead to a collapse of the party. For all sorts of reasons, this isn't going to happen.

The Prime Minister is appointed by the Queen on the recommendation of the outgoing PM. Under normal circumstances, this is relatively straightforward: it's the leader of the party which, alone or in a coalition or other agreement, can command a majority in the Commons (or failing that, is likely to survive a confidence vote).

However, in theory (and, in the distant past, in practice), the Queen could appoint anyone to the post if they have enough support in Parliament. There's even no requirement for the PM to be an MP (there have been a number of PMs who sat in the House of Lords), though it's unthinkable that that would be allowed these days.

Also, the convention is that an outgoing PM does not resign until a successor is in place. So for example, Gordon Brown remained as caretaker PM for 5 days after losing the 2010 election, until it was clear that David Cameron would head a coalition government.