People's Republic of Great Britain

The People's Republic of Great Britain, (TV: Doomsday, TV: Rise of the Cybermen) often simply shortened to either Great Britain, (TV: Rise of the Cybermen) or the People's Republic, (TV: Doomsday) was a 21st century nation and the government of Britain in Pete's World.

London was located in Great Britain. (TV: Rise of the Cybermen)

History
It was ruled by the President of Great Britain, who was killed by John Lumic's Cybermen in 2007 after he refused to fund the Ultimate Upgrade project. (TV: Rise of the Cybermen) He was succeeded by Harriet Jones, under whom the People's Republic took over the Torchwood Institute. (TV: Doomsday)

Behind the scenes

 * John Lumic's order that they "Set sail for Great Britain!", in which he more specifically means London, perhaps implies that the individual nation of England doesn't exist in Pete's World. The same could be said for Scotland and Wales, the other nations of Great Britain in the real world.
 * Though not given the full title "People's Republic of Great Britain" in dialogue, in Doomsday, Jake Simmonds — while inside the parallel London's Torchwood Tower — said, "Parallel Earth, parallel Torchwood, except we found out what the institute was doing and the People's Republic took control."
 * The People's Republic of Great Britain is not to be confused with the Republic of Great Britain, which existed on Inferno Earth.