One tenant vacates joint tenancy

Tenancy Types and Management

Hello, I have a joint tenancy in which one tenant has vacated (they sent an email to say they had vacated). I don%E2%80%99t think they served a formal notice to quit, but just an email saying they had gone and the remaining tenant could have the deposit.

The remaining tenant will not cooperate in signing a new lease, but otherwise meets theirs obligations (pays rent etc).

Can the remaining tenant just continue at the property on the original periodic tenancy or ultimately need I evict them as they won%E2%80%99t sign a new agreement.

I guess what I%E2%80%99m trying to establish is whether the original tenancy is still active, has the remaining tenant converted to a verbal AST or something else?

I presume this must be a fairy common occurrence, but haven%E2%80%99t been able to find much on it

Thanks for any help.