Its £80 to transfer the plate direct to another car or £105 to put it on retention for the year.
The quickest way to do it imo is to put the plate on to retention you should then get the retention certificate back and V5 with a new vehicle reg for the car this is 99% of the time the original reg. Then when you have everything in place for the new and car relaxed from the retention hassle walk into the local DVLA office and they will apply the private reg to the new car straight away over the counter free of charge.
Ben