I used a guy called Chris who works for First Class driving. He has taught loads of people in SE1 (he would regularly wave at or be stopped by people when we were out on lessons!)
I passed first time last sept so he must have been ok!
I found him through First Class' website which you can find on google. The price was reasonable as well, especially when block booking. It took me a year because I was such a nervous learner and it didn't bankrupt me!
Chris only works Mon-Fri but first class have other instructors in SE1 who probably work other days.