The UK CAA were instrumental on developing the CAD test!
Ricky well done on doing your research and finding out about it and good luck in your flying career.
The CAA have a list of approved flight training organisations broken down to who is able to provide what. I can't help on choosing for your PPL but continue your research for CPL/IR schools whilst you are deciding what to do. As various posters have suggested - visit places and speak to students, find out about the instructors. I know of one school (hundreds of miles from you) where the student had 4 different instructors in 4 flights.
All the best with your future flying.