I think there's only so much he can do, however.
As 1922 Ctee chairman he can receive no-confidence letters, he can call meetings with backbenchers, and he can relay some of what's discussed to the PM. But that's basically it.
Perhaps the better issue is when the King intervenes.
As I understand it, if there's a no-confidence vote in the Prime Minister in which case there must be a general election, but I think that may have gone with the Fixed Terms Parliament Act. But what happens if there's such chaos that it's clear that no one individual can govern? Presumably the King makes a best guess, appoints a caretaker PM and dissolves Parliament so there will be a general election.