While Great Britain managed to rule the vast majority of the Indian subcontinent by the mid 1800s, its conquest of India took overall three centuries.
Starting in 1612, Britain established some trading posts in several regions of India, which allowed them to gradually control larger lands around the cities of Bombay in the Northwest, Calcutta in the Northeast, and Madras in the South. Through negotiation and subjugation, they increased their domination of the region, with a rapid expansion that started in the late 18th Century. The United Kingdom maintained their sovereignty over the region until 1947, when British India was split between two new countries: India and Pakistan.
This map shows the progression of British domination over India.