The British royal has expressed her deep sadness over the incident.
Helen Holland (81) died after "suffering multiple broken bones and massive internal injuries", her son Martin Holland told the BBC on Wednesday.
She had been in a coma after the crash, according to her family.
The Metropolitan Police confirmed Holland's death in an emailed statement.
"The Duchess of Edinburgh is deeply saddened to hear that Helen Holland has passed away. Her Royal Highness's deepest condolences and sympathies go to all of Ms Holland's family," Buckingham Palace said in a statement.
Sophie, the wife of King Charles III's youngest brother Prince Edward, the Duked of Edinburgh, would privately get in touch with Holland's family, the statement said.
The police watchdog, the Independent Office for Police Conduct (IOPC), is investigating the incident, which took place in the Earl's Court district of West London.
The IOPC said in a statement last week it was reviewing footage from police body cameras and had taken initial accounts from officers involved.
It had no further information on Wednesday, while London's Metropolitan Police said it was cooperating with the IOPC probe.
"This tragic outcome is being felt by colleagues across the Met," Chief Superintendent Richard Smith, head of the Met's Royalty and Specialist Protection, said in a statement.
"Our thoughts are very much with the woman’s family and loved ones at this sad time."
