I believe that as long as you inform the DVLA that ownership has been transferred then you will not be liable for the tax.
New Car Tax Rules
What are the changes?
" The new car tax (vehicle licensing) rules mean that from 1 January 2004 the registered keeper of a vehicle (the person named on DVLA's record) remains responsible for taxing a vehicle (or making a SORN declaration) until that liability is formally transferred to a new keeper. To avoid liability for taxing it, the keeper needs to inform DVLA when the vehicle is off the road, or has been sold, transferred, scrapped or exported. Once DVLA has been notified about a sale/transfer or that the vehicle is off-road we will issue an acknowledgement letter, which should be kept as proof that the vehicle record has been changed. "
http://www.dvla.gov.uk/newrules/car_tax.htm