The car was taken from the supermarket car park in Kingsend, Ruislip on Tuesday around 9.30am while the owner went to the ticket machine, police said. Officers visited the victim at home shortly after a call at 9.50am.
The victim's granddaughter shared news of the crime and a photo of the old BMW on the Crime Awareness Group for Ruislip and Eastcote on Facebook later that day and this was shared by hundreds of people.
The next day a couple who live in Ruislip saw the post on Facebook and recognised the car in nearby Westwood Close, called police and ten minutes later officers had found the vehicle and a driver, who was arrested.
PS Sam Quinn said: “This is an excellent example of the public working with police to bring offenders to justice.”
The Met Police said in a statement: “A 49-year-old man was arrested at the scene on suspicion of theft of a motor vehicle, possession of Class A drugs, possession of Class B drugs and possession of an offensive weapon.
“He was taken to a west London police station for questioning. He has been released under investigation pending enquiries.”
After the post was circulated on Tuesday night it was spotted on various streets around the Ruislip area. Alan Palmer, founder of the crime awareness group in which the news was posted, said there were also two calls to the police non-emergency number with sightings before the 999 call that led to the car being found.
Mr Palmer said: “What a result, in less than 24 hours after going on the website members of the crime awareness group managed to find it and get it recovered by the police.
“It just goes to show the people power counts in the fight against crime.”
The victim's granddaughter has since returned to update her original post and thank the members who shared it so widely. There were over 250 likes and shares.
Mr Palmer said: “When we set out the group three years ago, this is precisely the kind of stuff we wanted to do.
“The couple who found it and called the police on 999 so they wouldn't have known about it had it not been for seeing on the crime awareness group.”
He said speed can be of the essence in crimes such as this and it had been an example where the rapid pace of sharing through social media proved highly effective.