Cannot Cancel Contract

We signed a contract for 24 months in Nov 2013 with ADT (I thought it was for 12 months) and have now moved to another house in June. The call centre told me I need to email a moving form to them to cancel, which I did on 11 June. Since then, they have told me I will be liable for my account until Nov 2015 unless I sign a new contract for my new premises. I have checked the CPA and their contract and they both state that you can cancel a contract before the contract expires as long as you send written notification 20 days prior and as long as you have paid all outstanding amounts until the date of cancellation (we are up to date with all our payments). I would like to cancel both the contract for the old premises and the new one as I do not think it's fair to force someone to sign a new contract just because you moved and according to the contract and CPA I should not be liable once I have given written notice.