If you buy a new car and want to keep the same private number plates you have on your current vehicle then transferring them is a simple and painless process. Simply complete form V317 from the DVLA which will begin the process. Both registered keepers of the car (you and the previous owner) must complete parts of the application. When completed simply send the form together with an £80 fee to cover the cost of the transfer to the DVLA.
Available Personalised DVLA Cherished Number Plates in UK