Depending on budget, an S2000 or an Integra with a supercharger kit can be had for less than £10k.
Both with more potential the MX5, and both with easy bolt on performance parts.
There's a stoker kit for the S2000 that allied to a supercharger, will give you over 350bhp. The car itself can also lose about 100kg's of mass pretty easily, with a further 100kgs if you fully strip it out and add a carbon bonnet(12kgs saving there alone).
If you look at the suspension, there is a bevy of options, all in the MX5 ballpark too. A good set of coil overs can be had for about £900, and I'd recommend it, as well as brakes which will set you back £950 quid for discs pads and calipers(optional).
Standard, those brakes are fine and pretty much fade free for a 20 minute track session(mallory park).
But horses for courses, and with 350bhp, you'll want to stop predictably.
You'll likely need 17 inch offset wheels, Rota(fighter)do a range that are cheap and lighter than the standard 16inch wheels(marginally).
Your problem will come when it rains, as it will be tail happy. But an MX5 with 250bhp will suffer the same issue.
With this in mind, as well as the rules....could you run a 2.5 litre 400bhp Skyline for 8k?
http://www.ebay.co.uk/itm/1995-Nissan-s ... Sw9IpXxDn4