You can instruct your new provider to take over your services, who in turn will contact TalkTalk and they will accept his as sufficient notification but if the transfer date is prior to your contract end date you will be charged early termination fees.
http://help2.talktalk.co.uk/about-cancelling-my-talktalk-service
15.1 If you want to end a service or your agreement with us, please contact us (see paragraph 19
below). If any service is in its minimum period, you may have to pay a fee as set out in
paragraph 4.2.
15.2 If you want to end a service or your agreement with us outside the minimum period you will
have to contact us in writing or by phone to give 30 days’ notice; however, if you’re
transferring to another telephone or broadband provider, we’ll accept that you’ve given us
sufficient notice when we receive notice from them.