I could see
@twovultures suggestion coming about from an infatuation with the Roman Empire, and deciding to copy the princple they had with non-citizen subjects who joined the army - deploy them as far as possible from their native culture and language.
But I think
@Madhukar_Shah has a more likely approach. Based on how British authorities ran colonies across the world, the whole reason they wanted local administrators was to
translate into and from the local language - having them handle all the paperwork is more of a bonus outcome than the initial driver. So I really can't see them sending Indian clerks and admin staff into regions where the language and customs are different, for that reason.
But if they decide to align administrative divisions more closely with dominant local languages, such that it's feasible to have more of the record-keeping and administration done in that language because the district no longer overlaps linguistic boundaries... That might be feasible. Once you get above a certain level the Raj would want records in English so that information can be reported upwards to English-speakers, but certainly local records can remain in the local language. That then gives you a clerical staff, a bureaucratic middle class as it were, who can regard themselves as well-educated white-collar people and build up some pride in their own group.
I think a lot of the problem you need to overcome is that of
prestige dialect, or language in this case. While the Raj rules geographical India, then the people at the top of society, those with all the power, speak English. That creates a strong driver fpr any local who wants to climb the ladder, and obtain as much power as the British wil let them have, to learn English to gain access to the circles of power. So then the
local elite are also seen speaking English, which creates further pressure for people below them to also learn it, so as to ingratiate themselves with them, or to be seen as more powerful, influential and prestigeous by everyone else around them. Then you end up with the children of powerful locals going to British private schools and universities and a pan-Indian mindset developing between them while they're all adrift in a sea of Brits and feeling homesick. (Having done a language degree and also found myself as one of very few Brits at a German uni, I know how fast and how hard that can hit.)
I think that to end up with an independent Bengal, Maharashtra, Tamil Nadu etc., you really need each language
and culture to retain at least some prestige during the Raj. You really need both. Then as independence movements grow, you'd have a local seed crystal in each region to grow e.g. a Bengali movement rather than a pan-Indian movement. You'd also have administrative borders that aligned with the aims of a more regional movement, I feel like that might also help.