2 months rent taken in advance instead of deposit, but tenant still wants monies

Tenancy Deposits

I ussed an AST to my tenants last year. I did not take a deposit, but two months rent in advance instead, and this is written into the contract.
One of my tenants has decided to leave the flat five weeks before the one year contract expires as their relationship with the other flatmates has gone sour. Contract finishes on 1 August, and last payment date was on 31 May to cover rent until 1 August. I reminded tenant that although they are leaving early they still need to pay me till end of contract, which they have done. However, they are now under the impression that I owe them a month's deposit back. Can they claim any monies back from me as a result of moving out before the contract termination date? Advice gratefully recieved.