We receive the details of the Registered Keeper directly from the DVLA, and it is the responsibility of the Registered Keeper to update the DVLA when the vehicle is sold.
It can take a few weeks for the DVLA to reflect changes to ownership, if this is the case you should request confirmation from the DVLA that the vehicle is no longer owned by you, and submit this with your appeal.
For more details on this process from the DVLA, click here.