The British Raj (1858-1947) was the period when Britain had control over India.
The Fifth Doctor brought Nyssa, Tegan Jovanka and Turlough to Calcutta on 31 December 1926 to see the second Unofficial Test match between All India and Marylebone Cricket Club (MCC), which was played in the city on that day. The MCC won the match by four wickets. The Doctor considered it to be one of the best cricket matches of all time. (AUDIO: The Emerald Tiger)
The Seventh Doctor, John Watson, and Sherlock Holmes visited Bombay during the Raj. (PROSE: All-Consuming Fire)
The Tenth Doctor and Donna Noble were in Calcutta when the conflicts which led to the end of the Raj were happening. (PROSE: Ghosts of India)
The British eventually partitioned India in August, 1947. (TV: Demons of the Punjab)