It is indeed a matter of arithmetic Pops- clearly, but-
Since the Fixed-term Parliaments Act 2011, a vote of no confidence must be passed in a specific form in order to create the possibility of an early general election.
Under the Act, if a motion of no confidence in the government is passed , the house must then adopt a vote of confidence in that same or, as some on here would clearly like, an alternative government” within 14 days, or a general election is held.
But as defeat of a motion of no-confidence does not provide protection to the government in power for any specific length of time, the subsequent vote of confidence could come the next day?
But, it is likely (if not absolutely clear) that even rabid Remainer MP’s would not like to face the public at this point in time, and may not support a vote, so might wish to hold on as long as possible eg 14 days, before taking any action, but, the nuclear option could be used ie. it is entirely possible that he could prorogue Parliament again!
So, complicated as it all is, he could hold on for up to 14 more days ,from the first vote of no confidence, or of course, alternatively the Government could choose to resign of it’s own accord and trigger a General Election, or Resign and hand power to the opposition, without a general election – there is however no law which requires that the Government resigns.
The Act contains no provision regulating motions of confidence generally and it says nothing about whether or when a Government should resign in
response to such votes.
One of the most central rules of the unwritten constitution is that the Queen must have the benefit of ministerial advice.
Resignation by the PM would require that a new PM be chosen to form a new government – but who and from where?
It could , as you indicate, become a matter of numbers, and Corbyn would not command enough support, if he indeed survives the Conference?
Corbyn’s For the many not the few , is extremely hypocritical in that the few Remainers in the Parliamentary Labour Party are ignoring the many leavers in the Country!