Police were called at about 1.25pm to reports of a collision involving a car and a pedestrian on Madeville Road, near the junction of Moat Farm Road.
A police statement read: “Officers have attended and the pedestrian, a woman aged 28, was taken to a central London hospital suffering head injuries. Her condition is described as critical.
“The 26-year-old male driver of the car - a silver VW Golf - stopped at the scene. He was initially arrested on suspicion of driving whilst under the influence of drugs and taken into custody at a west London police station.
Madeville Road, near the junction of Moat Farm Road, courtesy of Google Street View
“He was further arrested on suspicion of possession of a Class A drug (believed to be heroin) and causing serious injury by dangerous driving. He remains in custody.
“Detectives from the Serious Collision Investigation Unit are carrying out enquiries into the circumstances of the incident.
“Any witnesses or anyone with any information are asked to call the collision investigators witness line on 020 8911 9555.”