Go get your ARDS National B licence test done first, if you haven't already. A good place to do it is Bedford, they're not overly strict there on the driving test part compared with somewhere like Silverstone.
Then go pick a race series! MX5 Championship is cheap but often over-subscribed, MR2 Championship slightly easier to get into but still full grids, or there's a ton of others. It's not cheap though, I reckon you're looking around £10K for a season including testing, parts, repairs, travelling, accommodation etc but still massively worth doing. I accept that number could be significantly lower or higher before anyone grabs me on it, I'm leaving it here purely as an average for the guy.
I don't follow much other club racing series, so there may well be better options out there, I'm sure the usual suspects will be by to add their knowledge to the mix as well soon.