In order to make things clear, I'm going to be asking "What if X people get the support of 100 MPs" and answer the question individually from there.
What if 4 people (or more) get the support of 100 MPs
Given that the party has under 400 MPs, this is not possible without some kind of mass defection to the party. As such, we will move on.
What if 3 people get the support of 100 MPs
This would mean that MP's get exactly one round of voting for these candidates. Whomever happens to get the fewest MPs supporting them would be dropped. Once two remain...
What if 2 people get the support of 100 MPs
If this happens, you skip right to the members vote. Members will vote, online, for whom they want to be leader. The person who obtains the most valid votes, wins. Questions remain how members who are offline (IE the elderly and poor) will be able to participate. The vote result is announced next Friday (the 28th of October 2022) and, shortly after the time of said result, (an hour?) the winner becomes Prime Minister
What if 1 person gets the support of 100 MPs
They become Prime Minister on Monday. (Oct 24th)
What if 0 people get the support of 100 MPs
Ahahahahaha. I'd laugh for starters. This would, however, be an utter disaster for the party. Not sure how they'd recover if this actually plays out. MPs would likely be desperate enough to back someone they hate just to ensure this does not happen. In short, the party may literally break apart if this happens.