Many years ago you could purchase a book that listed personilsed number plates so when you saw a reg such as MAG1C, PEP51 or AMS1 you could look it up and find out who the owner was. Don't know if it's still published.
DVLA will tell you if you have a valid reason for needing to know. Otherwise you can go on the plate sites, it may be for sale. Most of the sites act as brokers for people wanting to sell numbers who will reassign then when someone purchases, for example is the number on here: http://www.nationalnumbers.co.uk/