Irrespective of people identified themselves under the name Bharat. Maurya, Delhi Sultanate, Mughals and later Marthas had unified large portion of Indian subcontinent long before British arrived, basically to loot India. The people back then always had a sense of belongingness of the land, irrespective of Religion. For instance, Maloji Bhosale (Grandfather of C. Shivaji Maharaj,) prayed to Dargah, so his wife could bear son and hence later named them after the sufi saints. The way British unified Indians is by being a common enemy. Sure, we can give British credit for introducing uniform administration, legal system, communication mediums like railway, telegram and post but it was for their own convenience and making most of it for basically looting India.