You can search everywhere and still not find a registration number so often its easier just to register an interest with a dealer.
i.e. My name is John David Wilson, I live at number 5, birthday is Aug 1955 ideally I would like something like JDW, JW, AUG 55, but will consider anything up to £2,000
At the same time you can search yourself try the links below
Dealers (reputable ones anyway) share lists of reg numbers available so not only do they know where to look but which stones to look under.
In the above example the current format is probably the easiest (and cheapest) because DVLA do not issue the letter 'J' as a locator / memory tag therefore they are only available to buy whereas others (A, B, C, D, E, F, G, H, K, L, M, N, O, P, R, S, V, W, Y) are issued to new vehicles so your ideal number may be on a car somewhere and the owner is unaware you'd buy his number. So there are more 'J' prefix numbers available in the first place.
The obvious number for Mr Wilson to go for would be JW05 JDW, but there are other options (MW05 JDW = Partners initials, door number your initials) you can mirror this on your partners car (JW05 MTW) and may get a better deal buying two.