Provided that the tenant leaves on or before the last day of the fixed term of his AST, in law he is not required to give any form of notice. If he stays one minute after midnight of the last day of his lease, it becomes statutory periodic and can, in theory, run on for ever. Under these circumstances the tenant must give is landlord one month's notice that he intends to leave and his landlord must give at least two months. This notice should end on a "rent day" which is the day on which rent is normally due.
Any information given in this post is based on my personal experience as a landlord, what I have learned from this and other boards and elsewhere. It is not to be relied on. Definitive advice is only available from a Solicitor or other appropriately qualified person.