What would have happened if the British had not conquered India?

 ( from quora.com)

Balaji Viswanathan, History buff.

First, let me attack the myth that there was no India when the British came. Sure, in 18th century when the British conquered, India was a confusing mess of feuding states. However, it was not always like that. 

The name India might be foreign (From Persians) and relatively new (2500 years old), but even now in Indian languages such as Hindi the alternative name "Bharat" is more commonly used to refer to our nation. The term Bharat is probably 1000s of years old and used throughout the nation to refer to this land.  In Brahminical rituals we daily recite about Bharatavarsha (India) in Bharathakanda (Indian subcontinent) and these hymns in Vedas are 1000s of years old. Thus, the concept of India is neither new nor foreign. 

India during Mauryas in 3rd century BC(very close to the Indian map in 1947)

During Guptas (4th - 8th century AD)

During Palas in 9th century

Mughal empire (16-19th century) at its height

 
Marathas in 18th century (again quite close what is currently India)

As you can see in the map above, Maratha rulers already began to take charge of India by the time British came and the consolidation of India would have happened to reflect our historical unity.

It is hard to project what would have happened in a 300 year history. But, my guess is that:

1. India would have adapted to industrial revolution fast and Indian scholars would have built hybrid utilities to compete with European mills. India always had an edge in science during the rule of Guptas, Mauryans and other Indian empires and it is quite likely that the successors of Marathas would helped India compete with the West in science and technology.
2. India would have had far less famines and deaths that came with the rule of outsiders such as the East India company. Indian rulers of the ancient always had a good judgment of how much revenue to collect and when to collect (inappropriate) taxation was the main reason for many famines in India.
3. Indian Islam would have been absorbed within Hinduism as a separate sect. By the time of Bahadur Shah's regime, Muslim rulers were getting more Hindu'ized. For instance, many Persian scholars were translating the Upanishads and Vedas that eventually got the attention of European scholars. The Sufi tradition of Islam could have easily coexisted with Hinduism and we could have had a hybrid religion.
4. India would have had current Pakistan and Bangladesh stay with it, but it is quite likely that the Tamils and North East Indians would have stayed separate as they were never really a part of Indian empires as seen in the maps above.