The Doctor's reality (Doctor Who in an Exciting Adventure with the Daleks)

In Auld Mortality's universe, the Doctor asked Susan to come with him as he made his escape from Gallifrey, and the Possibility Generator detected several branching timelines in which she agreed, (AUDIO: Auld Mortality) including one where the Doctor and Susan came to live in Totter's Lane (TV: An Unearthly Child) and one where the Doctor and Susan came to live in Barnes Common. Both of these outcomes led to an encounter with the Daleks on Skaro. By the Barnes Common account, the Daleks were led by a Glass Dalek. (PROSE: Doctor Who in an Exciting Adventure with the Daleks, TV: The Daleks)

However, in the former telling of events, the Doctor and his new human companions first ventured to Stone Age Earth. There, the Doctor had a moment where he contemplated killing the injured caveman Za with a rock, but he was stopped by Ian Chesterton. That he was stopped from committing murder was a vital moment in the Doctor's growth into a defender of the cosmos, (TV: An Unearthly Child, AUDIO: To the Death) which his subsequent encounter with the Daleks further turned him into. (TV: The Daleks, Into the Dalek) In the Barnes Commons timeline, however, (PROSE: Doctor Who in an Exciting Adventure with the Daleks) the Doctor never had that moment with Za. (TV: An Unearthly Child)

Other parallel possibilities involved Susan saying no, (AUDIO: Auld Mortality) and further accounts showed the Doctor living a parallel version of the First Doctor's life in which Susan declined and the Doctor subsequently never met Ian Chesterton and Barbara Wright. (AUDIO: A Storm of Angels, PROSE: The Innocents)

Relation to other timelines
When attempting to use the fast return switch to return Barbara and Ian to Earth in 1963, the First Doctor noted that they may not necessarily end up in Totter's Lane, and might instead end up somewhere else, like Barnes Common. (AUDIO: Return to Skaro)

During the Last Great Time War, the Barber-Surgeon met a "version" of the Doctor who related that they had met Ian and Barbara following a car crash in Barnes Common. The War Doctor, however, related the version of events in the Totter's Lane junkyard. Upon being told of the version involving Ian's car breaking down, the War Doctor declared "that never happened", which the Barber-Surgeon replied to by noting "everything's happened somewhere". (AUDIO: The Horror) The Time Lords themselves were aware of multiple, alternative accounts of the Doctor's first encounter with the Daleks, all of which involved Ian Chesterton. (AUDIO: Sphere of Influence, PROSE: Dalek Combat Training Manual)

Behind the scenes

 * The Glass Dalek was illustrated by Roger Langridge for DWM 354.
 * The identity of the Barber-Surgeon is never made clear in The Horror, although he claims to have never been the Doctor. Still, he notes that the War Doctor has the dark potential of becoming "another" Barber-Surgeon. That the Barber-Surgeon knows of the Barnes Common account can be read as him being an alternative version of the Doctor, which would be supported by the Doctor Who in an Exciting Adventure with the Daleks not featuring the Doctor's first meeting with the cavemen and Ian preventing him from committing murder. In such a timeline, it would reason that the Doctor could develop into a much more brutal figure.
 * In the narrative trailer for He Who Fights With Monsters, the War Doctor notes that the Time War is spreading into his own past, which can be read as a possible explanation for how the alternative "version" of the Doctor arose.