Short answers, pulled from the story.
At its territorial peak in 1920, the British Empire controlled over 35,500,000 square kilometres, which was more than 26 percent of the Earth's land surface excluding Antarctica. At that point the empire's population exceeded 449 million people.
The territorial evolution of the British Empire is considered to have begun with the foundation of the English colonial empire in the late 16th century. The Kingdom of Great Britain inherited those colonial possessions when it was formed by the union of Scotland and England in 1707.
The Statute of Westminster 1931 converted the Balfour Declaration of 1926 into legal reality, granting Canada, the Irish Free State, and the Union of South Africa effective sovereignty. It ended the language of dependency on the Crown of the United Kingdom and established the dominions as sovereign international states.
India and Pakistan gained independence in 1947 under the Indian Independence Act 1947, which partitioned the subcontinent into two independent dominions. King George VI relinquished the title Emperor of India in 1948.
Fourteen territories remain under British rule as British Overseas Territories. The status received its current name under the British Overseas Territories Act 2002. Most are islands with small populations, and all with permanent populations have at least some degree of internal self-government.
Hong Kong was transferred to the People's Republic of China in 1997 as a special administrative region, under the terms set by the Sino-British Joint Declaration of 1984 and the Hong Kong Act 1985. The New Territories had originally been leased from China for 99 years in 1898.