The West Bengal-based charity's founder Aloka Mitra said she was "shocked" by the sexual abuse allegations against the Duke.
"It was a really scary time in my life", Ms Giuffre told the interviewer.
"He knows what happened, I know what happened and there's only one of us telling the truth". While it was the Queen who actually delivered the news to her favourite son and informed the rest of the Firm, Charles was said to be very involved in the decision.
Ms Giuffre - then called Virginia Roberts - alleges she was forced to have sex with Prince Andrew three times between 2001 - when she was 17 - and 2002, in London, New York and Epstein's private island in the US Virgin Islands.
The prince has always denied any sexual contact or relationship with her.
The Monarch will turn 95 in April 2021, the age her husband Prince Philip was when he stepped back from his royal duties two years ago.
As the story dominated British news for a week, overshadowing campaigning for the December 12 election, there has been widespread criticism of Andrew and demands he should answer questions from USA authorities about Epstein.
"In August 2019, following the death of Jeffrey Epstein, the MPS reviewed the decision making and our position remains unchanged", the police said.
The allegation related to trafficking to central London in March 2001.
The Met confirmed on Thursday that they had indeed launched the probe, interviewed Guiffe, got the advice from the Crown Prosecution Service, and decided the case was out of their jurisdiction to proceed with a full criminal investigation.
"Following the legal advice, it was clear that any investigation into human trafficking would be largely focused on activities and relationships outside the UK".
Metropolitan Police Commander Alex Murray said police concluded in 2016 after looking into the matter and consulting prosecutors that the London-based force was the wrong agency to investigate.
Prince Andrew - the Queen's third child - has been facing questions over his ties to Epstein, a USA financier who took his own life in August awaiting trial on sex-trafficking charges.
Earlier this month Charles laid a wreath on her behalf at the Remembrance Sunday service and the Duchess of Cambridge has taken on a number of her patronages including the Royal Photographic Society.