The Secretary of State has appointed a number of advisory panels to provide expert advice on the medical standards required for safe driving. The medical standards are published in a booklet, 'At A Glance Guide to the Current Medical Standards of Fitness to Drive', which you can download
here.
Responsibility rests with the Medical Advisers at DVLA to apply these standards and decide whether a person is fit to drive. The law governing the issue of driving licences is contained in the
Road Traffic Act 1988 and the
Motor Vehicles (Driving Licences) Regulations 1999.
The DVLA also produce this
Customer Service Guide for Drivers with Medical Conditions