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 them, he would have taken over Great Britain as its dictator. (NA: Timewyrm: Revelation)

In this timeline, the British Royal Family had been been executed before 1943 following 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 Third Doctor's arrival in this universe, 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 tried 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: the Time Lords decided to exile the Doctor to Earth in the late 20th century and the changes to the timeline would have happened much earlier. (The Time Lords had specifically taken away the Doctor's ability to time travel.) This however can easily be explained by several differing details surrounding the Doctor's exile in the parallel universe; i.e. the Doctor was exiled at an earlier date than the Third Doctor from our universe. One such (alternate) Third Doctor arrived later than intended (the late 1990s) in an Unbound story Sympathy for the Devil.