If you haven't signed a new tenancy agreement then you are on a periodic tenancy and the notice is indeed one month (there is a slight grey area here as some argue that the one month notice should coincide with the end of a rent period). The fact that the landlord has sent you a new tenancy agreement doesn't come into it unless you actually sign it.
I suppose the simple solution is to ask the landlord to show you a current tenancy agreement signed by you. If, as you say here, he can't then you are obviously on a periodic with one month notice.