Joint Tenancy - removal/change of tenancy

I am a landlord but have a query relating to someone I know who is renting via a letting agency.

6 month AST (in joint names). The 6 months has expired so the tenancy is on a rolling contract. The couple have split up. Tenant 1 has remained in the property and has continued to pay the rent and wishes to stay there. Tenant 2 has moved out and just wishes to have their name removed from the tenancy.

The tenants have contacted the letting agent and asked for Tenant 2 to be removed and a new tenancy to be issued in a sole name for Tenant 1. The letting agent refuses and says tough.

I have regularly over the years issued a transfer of tenancy but this letting agency refuses as says what’s the problem with someone’s name being on the tenancy who doesn’t live there.

Any advice as Tenant 2 wants their name off the tenancy.