We receive Registered Keeper details from the DVLA, and it is the responsibility of the Registered Keeper to notify the DVLA the vehicle has been sold.
You can notify the DVLA here:
https://www.gov.uk/sold-bought-vehicle
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.