Nothing wrong with P basses. Perhaps a little expensive for a first bass? Not everyone gets on with the P-bass neck (I don't).
You should be able to pick up something very playable for £250-ish, especially if you try the For Sale forum here. Ibanez SR300, Squier P or J basses, Peavey Milestone III would all be decent starters, especially if you buy second-hand from someone who knows their stuff. The Westfields are decent for the money. I hear good things about the new Revelations.