British have a profound effect on India's history but have not taken over the land in its entirety, despite the fact that India continued to become a British for nearly 100 years after the Indian Mutiny (aka 'Great Rebellion' and 'First War of Indian Independence', 1857-1858).
From 1858-1947 Britain ruled about 60% of Indian directly and the other 40% indirectly through native princes who followed British policies. During their time in India, the British developed tea and cotton agriculture and coal and iron industries. In fact, by 1940, the Tata Iron Works was the world's largest Iron factory.
Likewise, the British continued developing India's infrastructure with more railroads and telegraph lines, so that by 1900 India had the longest railroad in Asia. British administration and bureaucracy were efficient, as was the British style education system Britain established.
India gradually came under British rule, not by the efforts of Britain's government, but by those of the British East Indies Company, founded in 1599 by a group of merchants in search of nothing more than "quiet trade."
However, circumstances would thwart these peaceful intentions, and British would find themselves more and more in the role of conquerors and governors than traders. The consequences of Indian Mutiny marked the nature of political, social and economic rule that the British established in its wake.
By the end of 1858, the British had finally restored order. The immediate result of the mutiny was a general housecleaning of the Indian administration. The East India Company was abolished in favor of the direct rule of India by the British government. Another significant result of the mutiny was the beginning of the policy of consultation with Indians.
For further reading, see links below:
www.bbc.co.uk - From Empire to Independence: The British Raj in India 1858-1947
www.crf-usa.org - The Great Rebellion of 1857 in India
www.britannica.com - Indian Mutiny