Inferno universe

In one parallel universe, Great Britain was a Republic governed by a Fascist regime.

History
As the Doctor would later recall, prior to his exile on Earth, the Time Lords had offered his second incarnation a choice of bodies into which to regenerate. If he had chosen one of those choices, he would have taken over Great Britain as its dictator. (NA: Timewyrm: Revelation)

In this timeline, the the British Royal Family had been been executed at some point prior to 1943 in the aftermath of a Fascist revolution sympathetic to the Nazis. The British contingent of the United Nations Intelligence Taskforce was a sinister state security organisation known as the Republican Security Forces, Brigadier Alistair Gordon Lethbridge-Stewart was known as Brigade Leader Lethbridge-Stewart, Liz Shaw as Section Leader Elizabeth Shaw and John Benton as Platoon Under Leader Benton. Shortly after the Doctor's arrival on this world, Stahlman's project caused massive volanic eruptions all over the world. The Doctor believed that everyone on that Earth had died. (DW: Inferno) However there were many survivors, including the leaders of the major nations, who attempted to invade the Doctor's world and take the place of their parallel selves. (PDA: The Face of the Enemy)

Behind the scenes

 * The information revealing an alternative version of the Doctor as the dictator of this timeline in Timewyrm: Revelation by Paul Cornell presents a problem, as the Time Lords decided to exile the Doctor to Earth in the late 20th century and the changes to the timeline would presumably have happened much earlier. (The Time Lords had specifically taken away the Doctor's ability to time travel.)