I think it's one of those things where the rules aren't the same both ways, although they probably should be.
It probably is a numbers game. Think about the number of white people with European parents who are born and raised in India. It's a very small number and there's a high chance that their parents are diplomats, or people working on an expat contract, who haven't deliberately chosen India as a place to immigrate to and perhaps don't plan to stay forever. Their children probably go to international schools in places like Mumbai, rather than attending the local primary. So, a vanishingly small number of people to start with, and the number who actually attempt to assimilate with the local population, speak the local language fluently and so on, is even smaller.
Then think about the vast numbers of Indian people who have settled in the UK, in large communities with extended families, shops and restaurants selling Indian food, products and clothes, their own places of worship and so on.
If there were only a handful of Indians living in the UK they'd probably be considered Indian by everyone even if they were born in the UK, but because there are so many people of Indian origin living in the UK, British Indian has become an identity in its own right, meaning people of Indian origin who are born and raised in the UK and highly integrated into British life, but have that particular ethnicity and usually speak the languages of their extended family and have retained their Indian religious and cultural customs.
But until there is an equivalent number of white British people settling permanently in India, the odd person who does that will remain...well, odd. And will probably never be considered Indian. The best thing they can do is to marry and have children with an Indian and then at least their children will fit in a little better.