Tenant just upped and left. What notice do i give to formally end the tenancy

My tenant left without notice on 1 September. Did not tell me. I did not find out until 10 October. She let her cousin move in (without asking me first). The cousin is now in there with a proper AST.
What formal notice do I need to give her to legally end the first tenants tenancy? I still have her Deposit and she owes back rent from some time back. Thanks everybody