Understanding Council Tax Liability During Tenancy Overlaps

Hi,

The council have sent a council tax bill and is insisting that the landlord pays, even though the bill relates to a period just before a tenancy ended. Do you have advice on council tax legalities?

The tenants bought a house which is why the tenancy ended. I understand that you can be responsible for two homes.

I think the council are mixed up, thinking the tenancy home is a 'temporary' home or that they are not resident-tenants, where I know this might change responsibility. Surely the tenancy home would be their primary home, and the purchase become their second home for the month overlap?

Is there something I can quote as a solid response or an explanation I can give to explain the council is mixed up?

Thanks!