Hi Terry,

This is straight from the DVLA:

What to do if you are selling your vehicle privately to someone that does not have a GB address
You should fill in sections 6 and 10 with the new keeper’s name and address.
Both you and the new keeper (buyer) must sign and date the declaration in
section 8. Give the whole V5C to the new keeper to aid registration abroad.
You should then send a signed letter to DVLA, Swansea, SA99 1AG giving
the vehicle’s registration number, the make and model of the vehicle, the
date of sale or transfer, and the name and address of the new keeper.

Once we know about the change of keeper, you should receive an
acknowledgement letter to confirm that you are no longer responsible for
the vehicle. If you do not receive the letter within 4 weeks, please phone
0300 790 6802. If you are deaf or hard of hearing and have access
to a textphone, phone 0300 123 1279 (this number will not respond to
ordinary phones).