I would definately recommend Roberts Driving School in Lower Road, SE16 (Tel: 020 7237 8912). Both my husband and I used them for our lessons. I passed my test many years ago but my husband passed with them just last year. I also know many others who have used them without complaint. Good luck!
I have been using Key Driving, who are not too bad, though they have a tendency to cancel lessons at short notice. I believe this is because other students have tests come through at short notice and the car/instructor is thus needed. This seems reasonable enough. Number is 020 7833 8303 (I think). About £20 a lesson at weekends, with (small) discounts for bookings of 10 lessons.
I initially booked lessons with The AA, but cancelled them after the instructor failed to turn up for the first 2 lessons.