one tenant of a joint AST wishes to be removed.

Tenancy Types and Management

Hello

I have a married couple on a joint AST which is in periodic. They have split up and he moved out some time ago but now wants to remove his name from the tenancy so that he can buy a house for himself. Whilst i am sympathetic to him his wife does not want this as she knows she can't afford the rent on her own ( there are 2 teenage children living with her). She has looked into getting social housing but we all know that isn't likely to happen unless i evict her and that will take forever and I dont wish to do this. Basically all i want to know is; can i refuse to remove him from the tenancy. thank you.