The deceased woman has been named as Yasmin Chkaifi, who was aged 43 and from Maida Vale.
The man has been named as Leon McCaskre, who was aged 41 and also from Maida Vale.
Police were called at 9am on Monday, 24 January to reports of a stabbing on Chippenham Road, W9.
Officers, the London Ambulance Service and London Fire Brigade attended the scene.
Yasmin Chkaifi was found at the scene with stab injuries.
Also at the location was Leon McCaskre, who had been struck by a car.
Both were pronounced dead at the scene.
Next of kin have been informed and Family Liaison Officers are helping to keep them updated and supported.
Post-mortem examinations will take place on Tuesday, 25 and Thursday, 27 January.
Enquiries are under way to establish the full circumstances, but we can confirm the two deceased were known to each other and had previously been in a relationship.
A 26-year-old man, the driver of the car, remained at the scene and was arrested on suspicion of murder.
He was fully cooperative with the investigation and has been bailed to return to a police station on a date in late February while the evidence is evaluated.
Detective Chief Inspector Neil Rawlinson, of the Met’s Specialist Crime Command, said: “We are gaining a clearer idea of what happened at the scene thanks to information supplied by the public and by reviewing CCTV. Firstly, it is apparent that members of the public bravely tried to intervene to stop the attack and their actions were very courageous.
“We are speaking to the families of those concerned and doing all we can to support them at this terrible time. We can now confirm that both the deceased were previously known to each other and there are no outstanding suspects.
“A man, who was the driver of a car, has been arrested and bailed for a very serious offence and we must carry out a full investigation, looking at all the circumstances. I would ask the media not to speculate on the causes of the deaths while we are awaiting the outcome of two post-mortems, it is important that we deal with facts.
“Lastly, we appreciate the support we have received from the public. A number of people have already come forward, but we are still asking for anyone who has not to make contact with us. Any information could be vital in helping us fully understand why this dreadful incident happened.”
Any witnesses or anyone with any information is asked to call police on 101 or contact via Twitter @MetCC. Please quote reference CAD 1496/24JAN.
To give information anonymously contact Crimestoppers on 0800 555 111.
