... many Indians from different regions speak English to each other in India.
I believe you have a mistaken impression of Indians today, though you are likely to be correct in the long run
I've traveled through 6 major cities last year (Bangalore, Chennai, Hyderabad, Delhi, Pune & Mumbai). For the most part, it seemed that the university educated spoke English, but I found that the masses did not. For example, the auto rickshaw drivers rarely spoke English. Hindi is by far the most popular language in the north-central (aka Hindi Heartland) region of India and so the masses don't need English. In the south there are many different languages and dialects, but the uneducated don't travel as much so they don't have much reason to learn English or Hindi for that matter. As Indians become more affluent, I'm sure they will learn a bridge language, but it may be Hindi, not always English.
"May your future be limited only by your dreams." -- Christa McAuliffe