Every driving instructor in Britain is individually tested, qualified, licenced, enhanced criminal record checked, regulated by and registered with a government body called the DVSA (Driver & Vehicle Standards Agency), not by any driving school. The DVSA also conduct all practical driving tests for all licensed vehicle categories.
Driving schools themselves are completely unregulated. It may surprise you hear that RED, BSM, The AA, Bill Plant etc. just act as booking agents for driving instructors who are self-employed.
The best way to choose a driving instructor is by their personal reputation and reviews.
Please see my reviews here: