In a parallel universe visited by the Third Doctor, White Russia was the state of Russia during the 20th century.
Under the leadership of Joseph Stalin, Russia was a close ally of the fascist Republic of Great Britain. Europe was divided between these two vast spheres of influence. This state of affairs meant that World War II never happened as Russia and the British Republic were able to crush Nazi Germany by intimidating Adolf Hitler into backing down from his sabre-rattling.
The Russian-British alliance, which still existed in the 1970s, was one of Stalin's greatest legacies. By this point, Russia and Great Britain were both members of the Conclave, a super cabinet composed of the leaders of the parallel Earth's five continents designed to ensure world peace, alongside the American Confederation, India and the Asian Co-Prosperity Sphere. (PROSE: The Face of the Enemy)