Inferno universe

Accessed via a power accident at the Inferno Project, the Third Doctor discovered a parallel universe where Great Britain was a republic governed by a fascist regime.

Although some details were known about the history of this world, the Third Doctor personally experienced it only in the environs of its version of the Inferno Project.

The Third Doctor described it as a "parallel space-time continuum" (TV: Inferno) whereas the Seventh Doctor called it an alternate timeline. (PROSE: Timewyrm: Revelation)

Creation
The Sixth Doctor believed the Inferno universe had only diverged from the primary reality about fifty years before he entered it in the 1970s, (PROSE: The Quantum Archangel) although no incarnation of the Doctor was present when Marianne Kyle confirmed that the first known divergence was in the 19th century. When his conversation with his third incarnation's persona revealed the identity of the British President, the Seventh Doctor wondered if the Timewyrm had any part in creating this timeline as part of her efforts to weaken him. (PROSE: Timewyrm: Revelation) Another account speculated that the Inferno universe was the original timeline and the prime universe was a divergent timeline created by the Great Intelligence. (PROSE: Night of the Intelligence)

19th century
The Confederate States of America won the American Civil War during the 1860s. In the war's aftermath, the American Confederation was established. (PROSE: The Face of the Enemy)

Early 20th century
In 1921, the Russian Civil War ended with the defeat of the Bolsheviks. (PROSE: I, Alastair) Joseph Stalin did not join the Bolsheviks in this universe and later become the Prime Minister of monarchist White Russia. (PROSE: The Face of the Enemy) By the 1950s few Bolsheviks were still alive (PROSE: The Schizoid Earth) and communism had lost all credibility as a political ideology. One theory was that the defeat of communism left no strong left-wing bulwark, allowing for greater conservatism and militarism on the European continent. Britain would remain more liberal until the Great Depression undermined the mainstream parties. (PROSE: I, Alastair)

Professor Edward Travers was thought to have died in Tibet in 1935, before ever seeing the Yeti. John Mackay survived the trip and later worked for the British Army. (PROSE: The Schizoid Earth) Travers would have instead survived to work for the Republic. (PROSE: I, Alastair)

Oswald Mosley would form a political party simply called the Party, which had no real ideology besides the desire to take and wield power; streetfighting would rage in London between Party-supporting republicans and democrats, further undermining the government. This universe's Doctor was exiled to Earth in the 1930s and became an associate of Mosley, and the two operated out the Revolutionary Arms pub. The man was assassinated in 1936 and the Doctor seized control of the Party, spearheading the fascist revolutionary movement throughout Europe. It ran on the propaganda that Britons had been promised things and then betrayed by their rulers. (PROSE: I, Alastair)

The Second World War never happened since Adolf Hitler was assassinated during a military coup by the Wehrmacht in 1938. (PROSE: The Face of the Enemy)

The Party took violent control of Britain, slaughtering many of the old political figures and burning the Houses of Parliament. The Royal Family were executed in 1943 after being implicated in Mosley's assassination. (PROSE: I, Alastair) Brigade Leader Alastair Lethbridge-Stewart spoke of their deaths with relish. (TV: Inferno) In the wake of the revolution Britain never decolonised, retaining her colonies in Africa, Asia and the Caribbean, although Australia broke ranks and did not march to the Empire's new fascist tune.

1943 onwards
The Party would enslave and deport all non-white Britons (labelling black ones as "African") to the Carribean to work as plantation labour, banned jazz as decadent, and blocked imports of European alcohol & cars so they could maintain control of revenue from local product. Jazz and illicit beer were available in the underworld, enjoyed even by regime figures at secret bars. Curfews would be put in place and patrolled by the Auxpol Militia, who outranked the regular police. Military intelligence and secret policing was overseen by the Security Directorate of the Republican Security Force(PROSE: I, Alastair) and was overseen (as was espionage) by the Director of External Security, which by 1959 was Gordon Lethbridge-Stewart.(PROSE: The Schizoid Earth) ExSec was rivalled by the Directorate of Internal Affairs, an overlapping agency & controller of Auxpol that they had turf wars with; this was headed by Director Paula Hipwood. Internal Affairs also ran the Vault. (PROSE: I, Alastair)

The Republic of Britain and White Russia took the opportunity to divide Europe between themselves. Meanwhile in Asia, the Japanese successfully built their Asian Co-Prosperity Sphere (PROSE: The Face of the Enemy) though by 1959, "the Chinese" were used interchangeably with the Co-Prosperity Sphere. (PROSE: The Schizoid Earth)

In the 1950s, British military forces had established bases in Germany and exchanged military technology with Russia. The government was increasingly authoritarian and paranoid about espionage, even from their tentative allies of America and Russia. (PROSE: The Schizoid Earth) This world's James Lethbridge-Stewart would later suggest that it was the lack of a Second World War against Nazi Germany that had caused this: the British people had no recent warning of what could happen if they started giving up their freedoms and had no need or desire to fight for them. (PROSE: Night of the Intelligence)

The Republic was surprised when the Alistair Gordon Lethbridge-Stewart of the regular Earth's 1969 accidentally ended up in their 1959. They suspected him of being a spy - mistaken his drugged references to the Korean War as a sign he was working for the Co-Prosperity Sphere - and interrogated him for four months. By the time he'd left, they'd become aware of a third alternate Earth using their world as a staging ground to send warnings through time and the Republican Security Forces was proposed to deal with scientific threats. (PROSE: The Schizoid Earth)

Shortly after its founding, the RSF fought the Bannermen in Wales, where they captured the Bannermen spacecraft and reverse-engineered the alien technology. (PROSE: The Face of the Enemy) Elizabeth Shaw chose to join the Army instead of pursuing a scientific career after she left university and the regime's ideology nurtured the sadistic and cruel side of John Benton's personality. (TV: Inferno) In cities like London, barrage balloons with the party logo loomed overhead. (PROSE: I, Alastair)

A serious accident at Windscale nuclear facility severely contaminated the Cumbrian countryside, killing the village of Seasca;e. This led to a ban on the construction of new nuclear power stations in Britain, which then led to the Party approving all manner of crackpot energy schemes to fill the gap. (PROSE: I, Alastair)

France used to cause problems for Britain's control over Western Europe, in particular the 1789 Resistance movement. The French went quiet after Britain shot De Gaulle and ensured France could keep Algeria as a colony.(PROSE: I, Alastair)

The Resistance in Britain blew up Nelson's Column in 1962.(PROSE: I, Alastair)

In the late 1960s, there was a colonial uprising in Aden that was put down by the RSF. Irish nationalists remained a problem for the regime. (PROSE: I, Alastair)

In the late 1960s, the Republic's economy grew far larger than its electricity supply and mining industry could support, Rolling blackouts, coal rationing and longer shifts at coal mines were instituted to try to solve the energy crisis. However these proved deeply unpopular with a public which had accepted the Party's regime as a reasonable price to pay for a high standard of living, resulting in rioting in many major cities and even strikes at coal mines, all of which were violently quelled. In need of a more permanent solution than shooting disgruntled coal miners, the government granted official approval to Eric Stahlmann's geothermal Inferno Project, which started work at the Eastchester scientific labour camp. (PROSE: I, Alastair)

The Great Intelligence launched an attack on Britain in this universe as well. Koschei, here having not become the Master, saved the world from the Intelligence, but his TARDIS was irreparably damaged. Koschei was then captured, tortured, and pumped for information for years by the Security Directorate. (PROSE: The Face of the Enemy)

The Resistance was still active in late 1968 Britain and formed an alliance with shapeshifting aliens. In an attempt to undermine the Party's image, the Revolutionary Arms was destroyed in a pro-democracy terrorist bombing, followed the day after by a dozen simultaneous terror bombs across London - thousands died. General disorder broke out, with a riot in Gateshead put down by mass murder, while the aliens infiltrated the Party by duplicating a Cabinet minister. During an alien attack at Downing Street that wiped out most of the Cabinet, Gordon Lethbridge-Stewart opportunistically caused the death of the Leader and usurped power himself - inadvertently helping the Resistance, who wanted a coronation of a new leader at the New People's Parliament that they could bomb. This was violently prevented by the RSF. (PROSE: I, Alastair)

After taking power, President Lethbridge-Stewart even resorted to forcibly drugging the young people who had joined a state youth organisation called the Republic Youth Army in order to impose his will on them. James Lethbridge-Stewart was alienated by his father's thirst for power and used Axos material to get himself and his family out of this reality. (PROSE: Night of the Intelligence)

Despite having caused his death, President Lethbridge-Stewart's regime claimed the Doctor's legacy for propaganda purposes, retaining his portrait in government buildings and continuing to issue posters emblazoned with his face. (TV: Inferno)

In the 1970s the world was effectively ruled by the Conclave, a parallel of the United Nations Security Council, made up of the leaders of the main continents. Great Britain represented Europe and Africa, the Asian Co-Prosperity Sphere represented Asia, and the American Confederation represented the Americas. India and Russia also had their own representatives. (PROSE: The Face of the Enemy) A parallel of UNIT was known as the European Axis Military Corps. (PROSE: Still Lives)

In 1974 after six years of work Eric Stahlmann was in the final stages of drilling at the Inferno Project. Australian mining engineer Greg Sutton was a political prisoner in Britain, forced to assist at Stahlmann's project. (TV: Inferno)

Shortly after the Third Doctor's unplanned arrival in this universe, an accident at Stahlmann's project devastated the entire surface of the planet within thirty-nine hours. (TV: Inferno) The only survivors were those in bunkers (including the Vault) space stations and on the Moon. President Lethbridge-Stewart was killed when the fallout from the disaster at Eastchester destroyed London. (PROSE: The Face of the Enemy)

While the Doctor and Jo Grant were visiting Peladon, the surviving leaders of this Earth started to cross over to the Doctor's world. They planned to kill and replace their counterparts, but UNIT — who were reluctantly working with — thwarted the plot. The Master allowed Marianne Kyle to escape, hoping she would cause trouble for the Doctor some day. (PROSE: The Face of the Enemy)

Behind the scenes

 * The world is never actually referred to as "Inferno Earth" in any known DWU story, though the phrase "the Inferno universe" occurs once in The Quantum Archangel. However "Inferno Earth" serves as a useful shorthand. It's a logical in-universe term, since the Doctor accessed that particular Earth at the Inferno Project — something the novelisation tells us is colloquially known as "the Inferno".
 * While spinoff media would greatly flesh this world out, there is no explaination given in the show for why the world is different. The fascistic iconography and mention of "Defence of the Republic Act 1943" was likely meant to imply to contemporary audiences that this is because Second World War had been lost.