Legally you need only give one months notice but I would need to check whether this should end on a rent day or not, havent got that info to hand, sorry.
Once the AST expires and you stay on in the property your tenancy become a Periodic Tenancy with the same terms as the 6 month contract apart from the landlord having to give you 2 months notice to vacate and you having to give 1 months notice.
So, yes, you would need to give notice of at least 1 month. You could have, however, moved out of the property without any notice at the end of your AST in October.