Police were called to Southend Lane, Bellingham on Friday, October 31 at 10.13pm.
It is alleged the car involved in the crash did not stop at the scene.
The pedestrian, a 65-year-old woman, remains in hospital in a life-threatening condition.
Michael McLaughlin, 38, of Heath Park, Buncrana (Republic of Ireland), was arrested on Friday, November 7 on a motorway in Northern Ireland.
He was arrested on suspicion of causing serious injury by dangerous driving and failing to stop after a road traffic collision.
McLaughlin was escorted to England, where he was interviewed at a south London police station.
He was later charged on Saturday, November 8 with causing serious injury by dangerous driving and failing to stop after the crash.
He remains in custody, and will appear at Bromley Magistrates’ Court on Monday, November 10.
Specialist are offering support to the family of the pedestrian.
Officers continue to investigate and are still keen to speak to any potential witnesses of the crash who may have information.
Anyone who can help is asked to call police on 101 quoting 9111/31NOV.
