Personalised and private number plate transfers have to go through DVLA and usually take around 2-4 weeks to complete depending on the situation of the registration mark at the time of the number plate transfer. You can either do a car to car number plate transfer in which you would need the documents for both vehicles (Original Log book, Original MOT and a photocopy of the Tax disc). You would need to fill in a V317 DVLA form and this needs to be filled in, in section 2 and 3 on the form and for this car to car transfer there is a fee of £80 to be paid to DVLA which needs to be sent to DVLA along with the vehicle documents and the V317 form filled in and signed.
If you own a private registration number and you have it on a retention document or a certificate of entitlement and you are the grantee or the nominee on the certificate you are able to place the registration mark on to a vehicle that is registered to either the grantee or the nominee on the document. The name on the log book of the vehicle you wish to register the private number plate to has to be either the grantee or the nominee name on the retention document or certificate of entitlement.
If the registration mark is on a retention document, this means it has been on a vehicle previously and then taken off and put on retention. If the registration mark is on a certificate of entitlement, this means it has never been placed on to any vehicle yet and it will be an original document issued from DVLA at the time of purchase.