11 January

On 11 January 1894, when the Eighth Doctor and Samantha Jones arrived in London, the Zygons were snatching cadavers from their graves. Working together with an old friend, Professor George Litefoot, the Doctor managed to save London from the unearthly "body snatchers". (PROSE: The Bodysnatchers)

In 1692, the First Doctor, Susan, Ian Chesterton and Barbara Wright arrived in Salem Village, Massachusetts. As the TARDIS needed its image translator readjusted, the Doctor made his companions exit the ship and explore outside. While they were outside, he intended to dematerialise, and come back using the fast-return switch after a month from his perspective of fixing it. (PROSE: The Witch Hunters)

On that very day in 1962, Meredith Roberts was born. (TV: Reset)

Behind the scenes
According to The Brilliant Book 2011, which is not considered a valid source on this wiki, the First Doctor encounterted Winston Churchill in 1911. He stepped out of the doors of the TARDIS, and told Churchill it was an honour to meet him. When Churchill informed him they had met before, the Doctor chuckled and said, "That's the trouble with time travel".