SECTION 21!! Please help confused tenant (cant find the answers here!)

Hi,

I am coming to the end of my tenancy agreement (it ends on 27th August 2012)

My landlord served me with my section 21 notice to quit when I signed the original tenancy agreement (giving the correct 2 months befor the end of the tenancy).

In my tenancy agreement it states that we are to give each other 2 months notice either way to end the tenancy.

I have now found a new property which I am moving to on the 28th August and have told my current landlord (giving him one months notice in advance) that I will be leaving his property at the end of the tenancy agreement (27th aug) HOWEVER, he is now telling me that I need to give him 2 months notice (and will therefore owe him another months rent if I leave on the 27th).

I thought that as he had already served me with my notice to quit then technically I can just move out at the end of the notice and dont even need to give him notice myself at all??

Am I correct? Or do I still need to give notice as well as him giving me the section 21??

any advice is much appreciated