If you're building a Caterham-type thingie, you wouldn't use a Miata drivetrain out of choice. The engine isn't great for power, and there are better candidates (and cheaper!) out there. Early Ford Zetec 4's are popular; strong conrods, and the engines are easily capable of 200+hp, NA. Tuning parts are also widely available, and decently priced. MX5 engines, on the otherhand, in England, aren't too easily tunable. Virtually all the parts have to be sourced from overseas, at great expense, except possibly cams. Kent Cams have acquired a set of Holbey profiles for the 1.6.
The quintessential amateur motorsport vehicle in England is possibly the Vauxhall Nova; every weekend, up and down the country, amateur racers meet for sprints and hillclimbs. Old style rwd Escorts were popular choices at one stage, but the entries are often dominated by tuned and battered shoppers. Something like a Nova 1.4 actually does pretty well. Novas and old Minis (1400 A-series though) used to dominate the sub-1700cc road going class I used to enter. This really is the grassroots of English Amateur Motorsport.