I’d feel like a member if I forked out that kinda dough to race round a track.
I know over here you can buy tuition and a lap on an off road rally course in either an Escort Cosworth, Mitsubishi Lancer or
a WRX STI for £120 for 1/2 a day.
There is also race tuition and car handling followed by racing around Silverstone in a Ferrari 355 (I think), or a Porsche Carrera for £199 for 1/2 day.
People are allowed to race on the track for a small fee, and you have to sign a disclaimer (basically an “If I crash I’m a bonehead and it’s all my fault”). I also think that to race on the track you need slicks, they don’t allow standard road tyres.
If it doesn’t work, jam a screwdriver in there and jiggle it about.