Tenant leaving early on 6 month contract

Tenancy Types and Management

I've used the standard 6 month short term assured RLA contract with a
tenant. The priod of the tenancy is Jan - Jun

They have paid 2 months in advance and a rental payment in January.

They have informed me they will vacate at the end of Feb due to personal circumstances and the need to return to their parents home.

I have informed them they are liable for rent and costs until I have a new tenant in place or I have sold the house.

They have asked me to count one of the advance payments as the rent due at the end of February.

Is this a reasonable request? I think in principle they should pay on normal terms until I have a new tenant.

What am I legally obliged and able to do? I assume they will be liable for council tax as they are officially still the tenant? If they leave without making payments is my only recourse the small claims court? - would I need to wait until April when I am in a negative balance?

Regards

Jason