The legal requirements in the UK state that only Approved Driving Instructors (ADIs) and licensed instructors under training are able to give paid driving instructions. If anyone else is offering paid instruction then they are in fact breaking the law and should most certainly be avoided.
The Driving Standards Agency (DSA) issue two types of badge:
A green octagonal badge displayed in the window indicates that the instructor is fully licensed and qualified.
A pink triangular badge indicates that the instructor is under training but not yet qualified. This still enables them to legally instruct however and may even mean a discount is offered. Ask the driving school when you phone for an initial discussion if this is something they offer.
Look out for one of these badges on the windscreen of the learner car where they should be prominently displayed, as this ensures the instructor is legitimate and lawfully able to instruct.
The Driving Standards Agency closely monitor the Approved Driving Instructors and their tuition, grading them from level 4 which indicates confidence to grade 6 which indicates an extremely high standard of tuition. This is a useful guide for a learner and allows for a choice based on standard of tuition.
Insurance is another important area of concern. Being a member of the Driving Instructor's Association means that the instructor has public liability cover of £5,000,000. This will undoubtedly be mentioned in advertisements or another badge may be displayed on the windscreen of the training car. It is recommended that the instructor or school have this level of insurance.