A political question

By convention, the Prime Minister is the leader of the majority party in the House of Commons (assuming there is one). But the Prime Minister is really whoever can command the confidence of the House, and the convention only exists because that's probably going to be the leader of the majority party. If there were a situation where the leader of that party did not have the confidence of the House of Commons, then he would cease to be Prime Minister, and someone else would have a go at forming a government. He would be expected to resign immediately as party leader, but there's nothing requiring him to do so.

So does this also apply to the Leader of the Opposition, a question which may be relevant in the near future. Is the Leader of the Opposition necessarily the leader of the largest party that's not in government, or is it in fact whoever can command the support of the majority of MPs from that party, which may not necessarily be the same? In other words, is it up to the Labour party as a whole or just the Parliamentary Labour Party to decide who it is? If Labour had a majority, then it would definitely be a matter for the PLP and not the party at large to decide who was Prime Minister.