Tenancy ending/new tenants

Tenancy Types and Management

My current tenant has advised they will hand in their notice as moving to a larger house when they find one, but have not put this in writing yet as cannot find anything large enough. I have found new tenants and realise I can give a months notice myself now as the contract is rolling over but if the tenant has no where to go, is it likely they will not go and no one is happy. They have been fine all the time so I want to work it out for all of us but do not want to have a void over xmas if I risk loosing my new tenants who will wait a bit but not for months.