1956

In 1956, France granted the North African colony of Kebiria its independence, but civil war quickly erupted in that country. (PROSE: Dancing the Code)

On 23 June, Eleanor Grainger gave her husband Edward Grainger a party for his 50th birthday. The party took place the day before his birthday. The Eighth Doctor and his companions Samson and Gemma Griffin arrived at his house to get rid of a ghost which had been haunting the family. (PROSE: Dear John)

During the same year, Elvis Presley performed on The Ed Sullivan Show, which was recorded in New York City. The Tenth Doctor and Rose Tyler attempted to travel to this date to view this event, but ended up being detoured to London on 1 June 1953. (TV: The Idiot's Lantern)

The Soviet Union invaded Hungary. (AUDIO: 1963: The Assassination Games)

Ian Chesterton and Barbara Wright met Janet McKay on the Isle of Hoy, Orkney, Scotland. Along with the First Doctor, they fought the Bog wraiths. (AUDIO: The Revenants)

Allison Williams began attending the University of Cambridge. (AUDIO: The Forgotten Village)

Alternate timeline
In an alternate timeline accidentally created by the Fifth Doctor, the RMS Lusitania did not sink on 7 May 1915 and a petty criminal named Eric Charles Vincent (who died in the sinking of the Lusitania in the proper timeline) killed Alexander Fleming in a botched robbery attempt in December 1927 before the biologist discovered penicillin. Without the protection offered by penicillin, Earth fell prey to new strains of meningitis and pneumonia in 1956 and the survivors never developed a space programme. Consequently, the Knights of Velyshaa were not defeated by the Earth Alliance in 3562 as they otherwise would have been. (AUDIO: The Sirens of Time)