That's actually true. In fact you can read that on Gandhi's wikiquote page - http://en.wikiquote.org/wiki/Mohandas_K._Gandhi [To Every Briton (1940)]

Actually non violence worked for more than one reason. Its also that the British, after world war 2 had no where the resources to control a massive country like India. It was also there purpose was done, and things were getting way out of their control. And it was better to leave honorably.