Helen Holland, 81, was struck on West Cromwell Road and Warwick Road in Earl’s Court on the afternoon of May 10.
In comments carried by the BBC, Ms Holland’s son, Martin said she died after sustaining “multiple broken bones and massive internal injuries”.
He said she fought “for her life for nearly two weeks… but irreversible damage to her brain finally ended the battle today”.
He said she was using the “safe route of [a] pedestrian crossing” when she was struck by the motorcycle.
The IOPC have been investigating the incident and said on May 19 they were appealing for witnesses and had taken CCTV from nearby properties for examination.
The IOPC regional director Amanda Rowe said on May 19: “Our thoughts are with the woman, who has sustained life-threatening injuries, and her family.
“We have been in touch with them to explain our role and will keep them regularly updated as the investigation progresses.”
Buckingham Palace said: “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.”