British government

The British government was the governing body of the United Kingdom. It was formally known as Her Majesty's Government or His Majesty's Government.

The government was head by the Prime Minister of the United Kingdom who was elected by a democratic vote. The Prime Minister and other ministers formed the cabinet who operated from the Houses of Parliament. Members of Parliament each had their own constituency. The Prime Minister resided in 10 Downing Street. (DW: Aliens of London, NA: The Plotters)

The Home Office was a department of the British government responsible for the order and security of the United Kingdom. (TW: Children of Earth: Day Three)

The Doctor had a long-standing connection with the British Government, consorting with monarchs (DW: The Beast Below), Prime Ministers, (DW: The Christmas Invasion) and other members. (DW: The Claws of Axos)

History
In the 1950s, the British government created Department C19. (MA: The Scales of Injustice)

In the 1970s, the British government sponsored the Inferno Project, led by Professor Stahlman. (DW: Inferno)

The Master used technology and hypnosis to be elected Prime Minister. The Tenth Doctor reversed time so that his time in office never happened. (DW: The Sound of Drums/Last of the Time Lords)

In September 2009, the British government sought to placate the 456 and destroy Torchwood Three to prevent them from interfering. (TW: Children of Earth)

In 2050, the British Government was somehow taken over by a Korven called Lomax who turned it into a corrupt, totalitarian government in preparation for the pending Korven invasion. By this time, government agencies MI5 and MI6 appeared to have merged together to form the Department. (K9TV: Regeneration)