If at the end of the AST neither party has given the required notice (you 1 month, and the landlord has to give 2 months) then the tenancy becomes periodic
automatically by law. You don't have to sign a new AST if you don't want to. The landlord then has to issue you a Section 21 notice to quit (with 2 months notice)
Basically tell them to get lost if you want to and let them issue a Section 21 notice (or give 1 months notice yourself). Sites like http://www.letlink.co.uk are a source of good information