Medics performed CPR in the middle of the road as they battled to save the man, but he was pronounced dead at the scene on Wednesday evening.
It is believed the jogger was struck at about 6pm as he tried to cross the single-lane road near the northern end of the bridge.
A man who witnessed the aftermath told the Standard: "He was flat on his back, in the middle of the road, a tube in his mouth, a male paramedic giving him heavy, urgent CPR.
“They were very hard pushes to his chest.
“I could see the driver speaking to police explaining and showing what had happened. He looked in his late thirties and was with a woman."
He added: “That crossing by Battersea Bridge is utter hell. I have complained about it for years. There is no gap in traffic lights for pedestrians."
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Greg Hands, the Conservative MP for Chelsea and Fulham, tweeted: “Very bad news in Chelsea. Being told by police of a fatal road accident at junction Beaufort Street with Battersea Bridge just after 6pm tonight.
“Thoughts are with the victim’s family and friends.
“More news as it comes in, but drivers would be advised to avoid the area.”
Pictures of the bridge on social media show dozens of police vehicles and ambulances behind a large cordon.
Something serious has happened on Battersea Bridge 🙏🏼 pic.twitter.com/Lm0GFG4449
— Joe Harakis (@JoeHarakis) January 13, 2021
Police said the bridge remains closed in both directions as they investigate.
A Met police spokesman said: “Officers attended along with paramedics from London Ambulance Service (LAS).
“A man was found seriously injured. Despite the efforts of emergency services, he died at the scene a short time later.
“Enquiries are ongoing to trace next of kin.
“The driver of the car stopped at the scene and is helping police with their enquiries.”
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