I've done a few "race school / experience" type things and most are rubbish – pointless, nannying, way too little time on track and seem solely designed for middle aged men to brag about later on down the pub. Anything that involves a single seater means they dictate exactly how fast you'll go so you can't get anywhere near the limits in the wet, let alone the dry.
The one exception was Palmersport. Pricey (at about £600 for the day when I went) but absolutely excellent. The instructors are great – mostly current racing drivers, one of mine was a British GT champion. They try to push you as far as they can in the time they have – if you're not going fast enough their brake override allows them to take the brakes off as well as on! Everything is timed with prizes at the end, the cars are driven very hard, but all maintained very well indeed. I worked up through Clio Cup racecars, 911, Caterhams, Jaguar XKRs, bit of a break for karts, then the Palmer JP1 (lemans-style racecars) which felt ballistic in comparison before being allowed out in the single-seater Formula Jaguars, which are so far removed from any road car you'll ever drive it's hard to explain. After that, a bit of Caterham head-to-head slalom racing and off-roading.
It was my 30th birthday present to myself and worth every penny – I'd go every year if I could afford it. Maybe next year. They do evenings and half days now so you can get into the JP1 / FJ cars plus a couple of others for a few hundred quid.
Else Bookatrack as mentioned with their Caterham hire are very good. More so if you go for a quieter track or weekday when they do open pitlane rather than sessions – they're happy for you and a friend to share a car which brings the costs down a lot.