Rent Query?

I am about to move house and I am a little confused. I live in Scotland which may differ to English Law on this, but would appreciate any advice. I paid a £500 deposit plus £500 rent for the first month upfront for my current property. The lease was a 6 months contract which has run out and I have handed in my 2 months notice for moving in January 2009. Now, my question is, do I have to pay my current landlord for the full month of January when the I will be handing the keys back on the 10th January? I have stated in the written notice that this will be the last day of the tenancy and all keys will be handed in then. I just feel that £500 is a bit much to be paying out for 10 days!! If it is not in the lease (which has run out anyway?) should I cancel the standing order and pay the landlord a proportion of the month for January? Or would I be in breach of the agreement? Help!!

Any advice?

Thanks for the advice, we have given the two months notice in writing as stipulated so will approach landlord- think they will try and hold out for a full month and from what I have heard they are reluctant to hand back deposits(I know some previous tenants!). Hmmm, we'll see what happens.