About notice (not a fixed term start)

[jp19]

My landlord wrote a tenancy agreement 2012 where it says: "needs to give 2 months notice". We had not a fixed term agreement to start with, it was just that from the start I pay monthly the rent and I need to give 2 months notice to end the tenancy. I understand that the law seems to say I only need to give 1 months notice if I pay monthly. So if I give only 1 months notice am I fine legally speaking? Thank you