Fowler&fowler; has thoughtfully invited me on my Talk page to comment. 
Nichalp says in the present thread "The term "British India" is generally used in popular parlance to separate independent India from British-governed India". I am sure there is some truth in that, but I think the reply is that Wikipedia shouldn't about "popular parlance", it is an encyclopedia and needs to be about scholarship, about detailed and correct information, sourced as well as possible. To put that more grandly, it is about educating the world. To illustrate this point, in the "popular parlance" of much of the world, "Great Britain" and "England" are much the same thing, but by education people learn the difference between them. To have an article on British India here, even one with much improvement needed to it, is a powerful tool in that process of education.
On Nichalp's suggestion that "British India" should be redirected to British Raj", I and others do not agree with that, for all of the detailed reasons advanced so far: please see the discussion here and also at Talk:British Raj. And I believe Philip Baird Shearer has said correctly somewhere above that there is a consensus against such a redirect. 
Fowler&fowler; asks "Would you be opposed to "British India" being redirected to this overview article, British rule in India instead of "British Raj?" " I, of course, am one of those who believe Wikipedia needs a discrete article, so I should be opposed. 
In general, I do agree with the "overview article" idea which has developed, and if I am invited to help in particular ways then I shall be glad to do what I can, but I do not believe 'British India' would be a possible title for that overview article, as the term has a correct meaning which is significantly less than the whole of India.  
One thought which I believe Fowler&fowler; had some time ago which does strike me as another possible compromise would be to merge Provinces of British India into British India. For reasons of space, the separation might one day be an advantage, but as matters stand at the moment this might be a rationalisation which could make sense to all of us?
I hope these comments are helpful.