The car could be paid for from the retained surplus which the DVLA is permitted from the sale of marks (desirable registrations).
All tax and other income from statutory payments goes to central Govt. to join the yield from all other taxes.

Hi - my name is Mike Orford, the Head of PR for SEAT UK. I can confirm that the taxpayer does not incur any cost whatsoever from the Ibiza Ecomotive prize draw with the DVLA. The cars are paid for entirely by SEAT UK. The partnership is good for us because it helps promote our sub 100g/km CO2 car to a very wide audience, and good for the DVLA because it encourages more people to renew their tax online, which is a method that actually saves the taxpayer money in administration.