According to one account, Barbara Wright met Ian Chesterton at a car crash site on Barnes Common shortly before they both met the First Doctor and were transported to Skaro. (PROSE: Doctor Who in an Exciting Adventure with the Daleks)
The policeman Bernard Whittam worked and celebrated his last working day there, next to where the Doctor's TARDIS first took the form of a Police Box. (AUDIO: The Last Day at Work)
When attempting to use the fast return switch to return Barbara and Ian to Earth in 1963, the First Doctor noted that they wouldn't necessarily end up in Totter's Lane, and might instead end up somewhere else like Barnes Common. (AUDIO: Return to Skaro)