private plates

Depends what you want, I've bought cheap Irish plates off ebay & had no problems so far.

I want 3 specific letters and the can be anything

Alan Smith ( snipped-for-privacy@none.com) gurgled happily, sounding much like they were saying :

Apart, of course, from driving around looking like the landlord of a particularly divey pub.

dvla might be a good start

Why?

Yep,

always the best place to start as the dealer's tend to load their commissions on top.

If you do find a plate with a dealer or on eBay, always check with the DVLA that they don't still have it, as a few eBayers have listed plates they do not even own.