The theft is alleged to have been carried out by a criminal ring trading in body parts.
Mr Cooke, who presented ‘Letter From America’ every week on BBC domestic and World Service radio for more than 50 years, died in New York in March 2004 from lung cancer which had spread to his bones.
His family has been told that before his cremation, body snatchers surgically removed the bones and sold them for more than US$8000 to a company supplying parts for use in dental implants and other orthopaedic procedures.
"I'm furious. I'm enraged. I'm outraged," his stepdaughter Holly Rumbold told BBC radio. "My stepfather is not the only one that's been used for this macabre purpose and people are making billions of dollars out of it."
In particular she is upset by the ramifications of the theft and said, "I'm most shocked by the violation of the medical ethics that my stepfather's ancient and cancerous bones should have been passed off as healthy tissue to innocent patients in their quest for better health."
"For example, someone with a damaged spine could have it repaired by implanting cancerous bone and paying thousands of pounds for the procedure and I think it's the wickedest idea I have ever heard of."
Ms Rumbold recalled that on the night Mr Cooke died, "the undertakers collected him, (and) his ashes, or what we thought were his ashes, were returned the next day."
"They were scattered in Central Park, who knows, maybe some of the ashes were his, how do you know? It defies the imagination."
The Daily News said that an investigation was being carried out by the Brooklyn district attorney's office into a tissue recovery business.
It noted that "after processing, Cooke's bones could have been used for
dental implants or numerous orthopaedic procedures including dowels for damaged spines."