The alacrity with which Boris was able to find a new Chancellor and new other ministers upon the abrupt resignations of the incumbents made me wonder if the persistent bobble-head-floating-doll tendency of the British government would keep him going. Remember that the resigned Chancellor, Rishi Sunak, had been appointed to replace his paired resigned minister, health secretary Sajid Javid, after the last time he resigned in total disgust at Boris's governing methods. Didn't prevent him from coming back.
However, it appears that the first thing new Chancellor Nadhim Zahawi did was tell Boris that he had to resign. Michael Gove, the only other minister with close to Boris's political weight, had gotten fired for saying the same thing, but I guess firing your new Chancellor the day after you appoint him would be a little too much. So with that and all the massive number of other resignations at cabinet and sub-cabinet level, now it looks like he's really going.
So what happens next?
The Conservative Party controls Parliament, so the next PM will be the new leader of the party. If the leadership is contested, which it probably will be, this could take up to a couple of months. But who knows: in 2016 the candidates kept dropping out, either through lack of support or because something unsuitable cropped up (either in their past or because they opened their mouths) and they wound up with Theresa May because she was the last one left standing.
So Boris could remain PM for a short but indefinite period.
If the revulsion is so great that he has to go now, there will have to be an interim PM until the new leader is chosen. That's happened a few times with the Labour Party leadership out of office, or with PMs in other countries, but never with a UK PM since this procedure was established.
The default candidate for interim would be justice secretary Dominic Raab, because he's deputy PM and that's what the deputy is for. But if he's a candidate for the permanent post, incumbency could be perceived as an unfair advantage and they might have to get somebody else, probably a senior semi-retired figure.
Whatever happens, it's liable to be very soon.