Doubt you'll get a P3 for that money but a P2 is definately on the cards. Great deck, very tweakable too; the RB250 arm is a prime candidate for upgrades, the you can add new replacement mats for very reasonable money (Achromat by Funk, Ringmat from Ringmat Development) and all manner of rewiring jobs to mains or interconnect to the amp.
Alternatively, trawl the web to see if you can still land a new or ex-display Goldring GR2 - basically a Rega P2 but with RB250 arm AND the brilliant Goldring 1012GX cartridge. Best deck under £300 when it came out two or three years back and you very occasionally see one appear in independent dealers. Originally £265, but I saw some for £220 earlier this year. To give you an idea of where we're at with this deck, the arm and cartridge retail for about £130 and £110 respectively. As the Yanks say, do the math...!
Other P2 variants include the NAD533 and these occasionally appear new too.
Older decks - if buying off Ebay be as sure as you can be with your the apple of your eye; check with the seller that "excellent" means excellent. Generally, you can find the aforementioned Pioneer PL-12D, but also other gems like the Systemdek-IIX, or IIX-900 which are great buys and also tweakable. Thorens is another to watch out for. Go for the TD160 over more recent decks like the (very average) TD-280-IV for instance.
Great vinyl replay can be had for relatively little outlay, spare £35 for a service (i.e. get the inner workings cleaned and re-oiled, etc) and £60 for a cartridge like the very popular (on here) Ortofon 2M Red or the superb Denon-110 and you'll have a deck that'll be a seriously good budget proposition.