British India was the areas of South Asia that were for hundreds of years under the influence of the English and later the British. From the 1600s to 1858, those areas were run by the East India Company. From 1858 to 1947, they were the British Raj. Some areas were under the direct rule of the Governor-General of India. He was appointed by the Government of the United Kingdom in London, and he was also called a viceroy since he represented the British monarch.
After 1876, when Queen Victoria become Empress of India, British India was part of the British Indian Empire, which also included hundreds of Indian princely states that had never been conquered by the British and still had control of their own affairs. They were ruled by local rulers under the protection of the British. They had almost half the land and a quarter of the people of the British Indian Empire. That empire is sometimes called the British Raj.
British India included the regions of the present-day Bangladesh, Republic of India, Burma and Pakistan (1858–13th August 1947).