BSM and AA are the top 2 nationwide recognized driving schools.
both of them have sophisticated training techniques in place to train you as a competent driver.
disadvantages :
1) most of them have a huge wait list , you may not get a slot unless you book months in advance.
2) Price per lesson can be upto 25 per hour where as you find local driving schools doing as low as 17 per hour.
if you have a US licence you can drive in the UK for 1 year with insurance. Within the 1 year time you you can take minimum required lessons and obtain your full UK licence thus minimizing the learning curve and cost.