Police were informed by hospital staff that a woman had been brought in by London Ambulance Service with a serious head injury.
It is understood that she was found at around 3pm on Friday (November 8) near to the High Road.
The woman, aged in her 30s, remains in hospital in a life-threatening condition.
Officers continue to work to establish what happened to the woman, and how she sustained her injuries.
A police spokesperson has urged anyone who was in the area at the time, or who might have seen the woman before she was injured that day, to get in touch.
Anyone who has information that could help police should call 101, quoting reference CAD 6099/8Nov.