Once, British Empire included India in its borders. That didn't make India part of England. Historically Indian sub-continent consisted of the following parts: Hind, Sindh and Deccan. Sindh ( The Indus and its tributries) is Pakistan. It was almost always a separate country or countries.Anyways, historic India is Indus valley that is contemporary Pakistan. Contemporary India is actually "Bharat". India should call itself Hindustan or Bharat. Word "India" belongs to Pakistan. Kashmir kept itself a soverign country untill Mughal emperor Akbar took advantage of civil war in Kashmir. Kashmir was never part of Indian culture and it will never be. Go and see in kashmir with your eyes wide open. Kashmiris look differnet from hindustanis in all respects. A true Kashmiri can not think of calling himself a " Hindustani". that means Kashmir is a separate entity from India.
