The victim, a 40-year-old man, was found suffering a single stab wound in Acton High Street at 8am on Tuesday.
He was rushed to hospital where his condition is unknown.
Shoppers were stopped from entering the area close to a Savers discount store by police.
A Met spokesman said: “Police were called to reports of a stabbing at High Street, W3.
“Officers, London’s Air Ambulance [HEMS] and London Ambulance Service [LAS] attended. At the scene a 40-year-old man was found with a knife injury.
“He was taken by LAS to a west London hospital. We await an update on his condition.
“At this early stage there have been no arrests.”
Officers were pursuing a car along Du Cane Road, near Shepherds Bush when it ploughed into another vehicle.
Those in the car ran when police moved in just after 8.30pm on Monday.
A man was found fatally injured on underground tracks after being hit by a central line train near East Acton station after the incident.
Anyone who witnessed the Acton High Street attack or has information should call police on 101 or Tweet @MetCC quoting 1589/22AUG.To remain 100% anonymous call 0800 555 111 or visit Crimestoppers-uk.org.