Private number plate transfers can all be done by the dealer in which you are purchasing the number plate from. Select provide a full transfer service like most other companies.
When buying a private number plate, it can either be provided on a Retention document, Certificate of Entitlement or you can have a car to car transfer. The vehicle has to be taxed and mot'd at all times to do this. On average number plate transfers take around three weeks to complete (give or take), depending on how busy DVLA are at the time.
For a car to car transfer the buyer and seller would both be required to provide the Original Log Book, MOT and a photo copy of the Tax disc, for the vehicle the number plate is being transfered from and to, these would need to be sent to the dealer in order to complete the transfer.
When the number plate is being provided on a Certificate of Entitlement or Retention document, the dealer would have the nominee changed, the nominee has to be the name on the Log Book for the vehicle you require the number plate to go on. Once payment has been processed the Retention document or Certificate would be sent out to the buyer and they would then be able to register the plate to the vehicle. You can do this either by taking the Retention or Certificate (which ever is provided) along with your Original Log Book, MOT and a photocopy of Tax disc down to your local DVLA office in person or you can send it to your local DVLA office in the post.
You are not allowed to put the actual set of number plates on your vehicle untill you have registered it through the DVLA. All private number plate transfers are logged in to the DVLA systems.