Have a look at www.firtreestud.co.uk theyre in East Yorks, but do training livery, specialise in starting and bringing on, have qualified staff BD Trainer, and BSJA, natural horsemanship and Classical Riding. They recently trained the Friesian Ridden Champion UK.
Youd probably get more value for your money for short term training livery as youd have to factor in traveling costs for sessions for any instructor.
Id say give them a visit, i have my horse with them, and ive seen a few come and go, and ive never seen a horse that hasnt loved it and settled in beautifully. Theyre very big on routine so that new horses settle in very fast.
I teach and cover your area (PM me if you want to know more lest I be accused of advertising) but I would be too big to ride a 13.3. As would most of the instructors I can think of in that area.