Well votes of no confidence generally result in a General Election. No need for any " government of national unity" ( complete misnomer), or for anyone to declare themself to be Prime Minister in the mean time.

Let's just dissolve Parliament in early September when it reconvenes and have a General Election in mid November, which is the normal period for an election campaign .

There's a "deal" for you, and I tend to think it's the most likely outcome.