Police had been pursuing the VW Golf, which had been taken by two men a few minutes before from an undisclosed location.
They broke off the chase after the VW and then the police car both hit a Vauxhall Zafira at the junction of Botwell Lane and Church Road, Hayes.
The VW carried on and was then in collision with a parked Vauxhall Frontera at the junction of Moray Avenue and Compton Road in Hayes, just as the driver, aged 70, was getting out, say police.
He died at the scene. The occupants of the VW Golf ran off.
Scotland Yard confirmed the Independent Police Complaints Commission (IPCC) and Directorate of Professional Standards have been informed about the incident.
This morning (Wednesday), police cars were dotted around the surrounding area. Several alleyways between houses on the road were taped off, and a crime scene officer was combing the area for any forensic evidence.
Moray Avenue resident Samaira Mahmood told the Gazette: "I went to pick up my son from an after-school club at around 6.30pm, and when I got back, all the emergency services were here. There were police helicopters, looking for the people who did it.
"From our window, we could see the man lying on the pavement, and paramedics were trying to bring him back, but they couldn't."
She added that the pensioner had only lived there for a short time.
"I saw him once or twice and he would just wave, he seemed friendly. It is really awful. Something like that can happen to anyone."
Met Police traffic officers are investigating. Detective Sergeant Chris Osborne said: "We are keen to speak to anyone in the area who either saw the Golf being driven prior the collision, or anyone who saw the people responsible running away afterwards."
If you can help police, call 020 8998 5319 or Crimestoppers. anonymously, on 0800 555 111.
More shortly. Please call the Gazette on 01895 451036 if you have any information.