Is this unjust enrichment or breaking a contract please read?
When people say “private sale” they normally mean selling without an Estate Agent not a solicitor. No-one can answer this unless they see the contract you both signed.You appear to have some legal knowledge or have had some legal advice already as few lay people use the expression “unjust enrichment”.However it would be reasonable to assume the contract has gaps as it has apparently no terms covering the current situation. The options are in my opinion :- 1) you had a concluded contract for the sale of the house to Mr.X at £165 with a deposit of £20K.If so he is bound to buy at that price and if he cannot he loses his deposit and you can in theory sue him for breach of contract if you have to sell later for less than £165K-£20K. 2) or you had a conditional contract subject to either completion of the improvements and/or Mr.X getting a mortgage.However you say the work was complete and Mr.X told you he could not get a mortgage -implying he had the cash.So it was probably a concluded con