India was already a country before the British rule and it was just made independent in 1947.
The Union or India came into existence after the independence.
However, this part of the land was always colloquially called India / Bharat for a long time before that. There was no single state of India, true.
But this was a collection of different regions with an ever-shifting / undefined border.
Aryavarta, Brahmavarta, Panchala, Braharishi Desha, Madhya Desha etc were all regions and within them there were many kingdoms.
Now I am no scripture expert and know these by heart but someone with the proper knowledge would be able to corroborate this.
Manav Dhramshastra in Sanskrit was quite possibly the first coded book of laws similar to the modern constitution. So you see the concept of India was always there.
The britts just came here and tagged all of us 'idies' and Indians and the land "India"
Hindustan however was a later construct when the muslims started invading.
They do,if you don't know about it then go and vist south India where is the only place people opposed Hindi as their main language even second language. 
Have to disagree here, BJP as a government never condones or says this. RSS does. BJP runs the government. RSS does not. However even a kid knows the connections between BJP and RSS.
Hindi should be an official language in places where Hindi is spoken, and regional languages should be given more preference.
But from an administrative point of view, I understand why so many people are so eager to push the one language one nation theory, stems from the us vs them crap. Hindi vs urdu. Hindi vs rest of the world.
The fact is, India has never been the land of homogeneity - it never will be.