Today, English is spoken by around 10% of India's population, and as best I can tell, it's the language of higher ed, corporate business, the bureaucracy, judiciary and maybe the national media. What would it take to make English spoken by 2/3 of the population (what it appears to be in Ghana)? I'm not suggesting eliminating any native language - just make English more of a lingua franca in India and make India by far the largest English speaking country in the world. I'd prefer to change as little as possible beyond that - keep India independent, etc.
This might have more of a chance in an undivided India where a larger Bengali and Punjabi population team up with South India to avoid to being dominated by the Hindi speaking region in the North. South Sudan is trying to change its foreign language education from Arabic to English right now. Arabic is associated with domination by Sudan, but Juba's elite sees English as a "neutral" compromise language that doesn't favor any of S. Sudan's ethnic groups. Greater English education would serve a similar "neutral" role to put all the country's different groups on a neutral playing field.
If India is closer to the United States for some reason in the immediate post-Independence period, English might be less associated with the Raj. If India's leaders take a more export-oriented development strategy instead of the License Raj, New Delhi may see English as a good way to integrate India into the world economy.
I think that India OTL definitely has a comparative advantage thanks to its large English speaking population. Millions of bilingual speakers of English and an Indian language (Hindi, Punjabi, Tamil, etc.) has made it easier for US pop culture to enter India, but there's also more of a two way street with India's massive diaspora and cultural exports. There are successful Bollywood films like
Chennai Express,
Slumdog Millionaire, and Bhangra singers like Daler Mendi who have had some success in the US.
I can't recall a Mandarin language film or Mandarin-speaking pop musician ever reaching comparable popularity in the US. China probably has a comparable or larger diaspora than India, but it seems much more closed off culturally.