Inferno universe

In one parallel universe, the fascist Republic of Great Britain had taken over the country.

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 royal family had been been executed. Here, Brigadier Alistair Gordon Lethbridge-Stewart was known as Brigade Leader Lethbridge-Stewart, Liz Shaw was known 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).

Survivors of the destruction attempted to invade the Doctor's world. (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.)