You're on a periodic tenancy, which happens after a fixed term agreement expires and isn't renewed but the tenant remains in situ.
The LL must give you at least two months notice and you must give one month, both ending on the last day of a rent period (although this last part is commonly ignored). It doesn't matter what the agent says, or indeed what it says or said in any agreement you had. The law overrides this.
If your original 6 month agreement had a clause saying the LL could give you two months notice to quit then this was legally incorrect and would have only been enforceable two months before the end of the contract i.e. for you to leave at the end of the contract.
This is all assuming you are on an AST (Assured Shorthold Tenancy) which most tenants are these days.