The two I know near you are Hargate and Barleyfields but I don't know what level the instructors are you possibly have looked at them already. The best way forward to improve your riding is to move away from school horses. Have you considered a loan horse or sharing I do know of people who look for you to ride and assist with looking after their horse generally.
Hi I have schoolmasters that I teach on in staffordshire. Fully licenced and insured. Horses are available for lunge lessons and beginners right the way through to Prix st George. Tolerant, quiet horses without being lazy.
I may have some alternatives for you if you live in Hatton we are about five miles away pm me if interested but it will be a step up from school horses.