There are sevreral types of personalised number plates that you can buy via DVLA site or go to a DVLA auction, which are prefix style plates, current style plates, suffix style plates and dateless style plates.

You can do a search on the link provided above. By entering your intitials, dates, or car models in the search box, the prices for different style plates will be displayed. The starting price for a personalised plate is £255. However, if its a poplular plate or if it goes to auction, it will cost a lot more depending on the bidders.

The prices displayed on DVLA site are full price incluing VAT and administration fees (i.e. currently £80). Once you make the purchase, you should get an email notification within 24 hours.

If you want more information regarding the purchase, you can check the DVLA's help page.