Hey, we could end like Belgium who didn't have a government for 535 days after their General Election in 2010 - 
https://brussels-express.eu/fun-fact...ut-government/
If Boris refused to go, I could see the Queen passing the buck to the Privy Council to sort things. There are some right characters in there - 
https://en.wikipedia.org/wiki/List_o..._Privy_Council