British supremacy rose in India because of their defeat of the Mughul Empire. At first the British didn't interfere with the Indian culture and religion, but when scholars arrived they wanted to "civilize" the Indians.
Some Hindus defended their religion, but some started to live by the Western standards. Hindu leaders realized they needed to be more thoughtful and adaptable in order for India to hold its identity. Hinduism was much later brought to the Western world indeed because of the forming of Indian nationalism and a missionary spirit which were needed to form the tradition of change and adapt.