Notice periods /What happens when an AST expires and the tenant is still there?

Tenancy Deposits

I am confused. I understand that an Assured Shorthold Tenancy has a minimum duration of 6 months and is for a fixed term. The agent I have been using seems to think that a landlord needs to give two months' notice if he/she required the tenant to leave for any reason prior to the termination of the tenancy. The AST is therefore acting as a binding contract on the tenant but not on the landlord? My tenant refused to renew her agreement because she did not want to sign up for another specific term, but my understanding is, that second and subsequent agreements between the same parties are still deemed to be legally valid if they include a provision for the tenant to give one month's notice of their intention to leave. I hope to take the rla course soon and perhaps this will answer that question. I already know that a Section 8 notice to quit is appropriate for an AST while a s 21 is for a tenant who has stayed on without an agreement and become a periodic tenant. In those circumstances I believe the landlord should give two months' notice while the tenant needs to give only one. It's really confusing. Plus my agent provided a 6 month AST which made no reference to the general terms of the tenany should that happen, ie once the AST has ended and the tenant is still in possession, which is what has actually happened. Am I right in thinking there may be an automatic carry over of basic terms (eg the obligation to maintain payment of outgoings) to the new tenancy or should this possibility be specifically provided for in the future?