All the tracks mentioned so far are decent.
Rye House (in Hoddesdon) has recently got an updated fleet of outdoor prokarts which aren't too bad. Not sure what pricing is like though. If you're just going for fun yourself, you can hire a Rotax kart (125cc watercooled, 0-60 in ~4 sec), although I think it's quite pricy. If you haven't driven a 2-stroke kart before, it'll blow your mind, especially into turn 1 (Stadium). (
http://www.rye-house.co.uk)
Streatham is an indoor track, and relatively cheap - £30 buys you an hour. The karts are generally ok (but can vary in standard by up to a second), and they've recently changed to dry clutches, so they have a bit more acceleration than your standard indoor kart. Although I haven't been for a while (I karted there when I was a cadet), I think they do some kind of Ironman/Enduro event for groups, which is quite cheap. (
http://www.playscape.co.uk)
All depends what you want to do really. If you want a cheap, indoor event, with fantastic karts (very fair, and quick for indoor machines) and grippy circuit, and willing to travel then there's a circuit in Aylesbury(
http://www.klubkartracing.com/)
edit - websites added - Also forgot to mention, Rye and Streatham are very close to train stations.