was almost 12 years ago when i passed my test (god i feel old now) but i had the same sort of problem, i started off with a small firm. (well was actually a bloke called alan who did it on his own who was recomended to me) I was with him for a couple of months.
I was havin a couple of lessons a week, he was basically gettin as much money out of me as possible. kept sayin he'd put me in for my test next lesson, and never did. this went on for about a month, so i changed driving instructors cause i got fed up.
I changed to a large well known company in liverpool called, A1 driving school, I had my first lesson with this guy called geoffry (great name lol) and he put me in for my test straight away. I was with him for about a month and passed first time. i also understood this guy a lot better, was much clearer in explaining things.
sayin that thou, dreamgirl passed her test not long ago, and had some lessons with the same guy i did (geoffrey) who I passed with, and didn't like him and changed instructers i think. so it's a case of if you feel comfortable with an inidvidual and understand them rather than how big the firm is.
All in all, it took me about 3 n half months and about 28/30 lessons after all the messin about i got from the first bloke.
dunno if thats any help, but thats my experience. good luck, sure you'll pass first time