tenant leaving early - can I use deposit for rent if he doesnt pay till new tenant found

Tenancy Deposits

My tenant is 3 months into a 12 month AST. He has said he is leaving as his car has been vandalised, there is damp in one of the kitchen cupboards and the kitchen lights have been flickering. He has not mentioned the points to us before hence we have not looked into the complaint, he has just said he wants to leave because of this.

I have told him that he will have to pay the rent until a new tenant is found and that he can leave early under that basis- I have used the rla deposit scheme AST. His rent date is 16th of the month and he wants to leave before the next rent and states he will give me money for advertising it again.

He is now starting to say that the property has lots of problems etc.., which is not true. My question is ..can i charge rent to him until it is rented again, and can I use his deposit for this? 2nd question is can I hold out giving him his deposit back until the property is rented, and give him back any that may be left?