Ok, so here's what I found.
I started by going to my save and counting provinces occupied. I found Italy had far more occupied provinces than Germany did. Something like 125 to 75.
Next I edited the save, giving Germany a bunch of the provinces Italy had. When I was done Germany had 98 UK provinces, Italy had 105.
NOTE THAT ITALY STILL HAS MORE.
Playing from that point the UK now surrendered to GERMANY.
So it seems occupied provinces is not by itself the answer.
My next thought was that maybe there was a requirement that you own at least one VP province, my editing had given Germany all the ones Italy held. To test this I edited the save so that Italian occupied Asyut had a VP value of 30.
This had no effect.
One other thing did change. When I gave Germany all those Italian provinces the Italian divisions sitting on them were immediately given to the German player as expeditionary forces by the AI.
So I next loaded the game up as Italy and elected not to do that. No effect, UK still surrenders to Germany.
Finally I thought maybe there was multiple variables at work here, and maybe both VP's and total provinces count in some fashion. To test this I edited the save to make Asyut worth 300 VP's.
Still no effect.
My conclusion is that I have no idea what the hell is going on.