After posting about Dr Ambedkar, I thought a bit further about the Indian independence movement as a setting for an adventure, and further about India as a setting at various points in its history.
The end of the colonial era and the independence movement is the part of Indian history you’re most likely to see in British media. Consider colonial nostalgia in modern Britain, for example. Britain’s relationship with India remains complicated, more than most former colonies. With a large Indian descendant population in the UK, the connections are still strong.
We should also think about how the Doctor and companions’ “Britishness” might lead people to make assumptions about which side they’re on if they visit during the colonial era.
Going further back, the religions most popular in India could be a source of characters, but give careful thought to how how they are portrayed. (For example, 18 Days from Graphic India, Grant Morrison and Mukesh Singh, is a superheroic SF retelling of the Mahabharata, intended to entertain an English-speaking audience while respecting the source.)