So many options! It sort-of depends what attributes are more important to you.
If ease of use (including things like speed change from 33 to 45) is paramount, then you can't go wrong with a well-looked-after Technics SL1200 or 1210. They normally go for around £200, leaving £50 for a good cartridge like an AT-95E or Goldring Elan. They sound great, are a doddle to use and are virtually bulletproof. Just avoid the ones without lids (been in a club!) and those that have been DJd - there are plenty out there, so be choosy.
For absolute sound quality, I would suggest a Systemdek IIX (normally come with the Rega RB250 arm) for similar money. A Linn Axis could also be a good bet (especially if it has the Akito arm), but there is a question over the reliability of the circuit boards, as they are getting a little long in the tooth now.
If you would prefer new, then the Rega RP1 has recently won a WHF award for best turntable under £300, and comes ready-to-go with a decent cartridge for £225.
My choice? See my signature...