It looks like we could have an unusual situation in the UK (well even relatively speaking)
On 23 July, the new leader of the conservative party will be announced. Traditionally the incumbent does not stand down unless they think their successor has the confidence of the house, but this is very difficult to know without testing it.
So potentially there could be a parliamentary no-confidence vote in the new leader on the 24-25 Jul. If this fails we would be in the 14 day period where the leader has to try and find a way to get a vote in the house that the can show they have confidence. Which is pretty well explained under the exceptions in the Fixed-term Parliaments Act 2011 (FTPA).
However, the house rises for its summer break on 25 Jul (note this is a break not the end of the parliamentary session) so the 14-day deadline for forming a new government can't be met. As far as I can see the FTPA specifies 14 calendar days, not sitting days.
What would happen in this situation, would the new leader just have to sit on their hands for 14 days before going to see the Queen and calling an election?