That tea is - for the most part - known as "chai" in India suggests a different origin (the world's languages are largely divided on the first sound in the word for tea: either Te or Ch).

It is true that the British brought large scale tea production to India, but the plant is endemic to India and its local consumption long predates the British (though the exact origins are somewhat obscure).

https://en.m.wikipedia.org/wiki/Indian_tea_culture