The prince has faced a series of scandals over recent years, including a court case he settled with Ms Giuffre.
Next week a posthumous memoir by Ms Giuffre will be published. It is likely to cast further attention on Prince Andrew’s involvement with her and Epstein.
Ms Giuffre claimed that she was one of many vulnerable girls and young women who had been sexually exploited by Epstein and his circle of wealthy connections.
She alleged that she was forced to have sex with the prince at the house of his friend Ghislaine Maxwell in London in 2001, when Ms Giuffre was 17 years old.
Her memoir describes two other occasions on which she alleges she was forced to have sex with Prince Andrew – in Epstein’s townhouse in New York and on Epstein’s private island in the US Virgin Islands.
In the book, she also writes that she agreed to a gag order.
Queen Elizabeth II was celebrating her platinum jubilee in 2022 – the first British monarch to reach the milestone – as the civil case against her son gathered pace.
“I agreed to a one-year gag order, which seemed important to the prince because it ensured that his mother’s platinum jubilee would not be tarnished any more than it already had been,” Ms Giuffre writes in her book.
Ms Giuffre’s brother, Mr Roberts, told BBC Newsnight: “We have shed a lot of happy and sad tears today. I think happy because in a lot of ways this vindicates Virginia.
“All the years of work that she put in is now coming to some sort of justice, and these monsters can’t escape from it – the truth will find its way out.”
He said this was “a moment where survivors are not staying quiet any more”.
“It’s just a joyous moment for them because we’re finally getting some sense of acknowledgement, like ‘this actually happened, what we’re saying is the truth’,” Mr Roberts added.
He said there was “so much more to be accomplished, especially here in the United States”.
Haley Robson, a survivor of Epstein’s abuse, said the prince losing his titles was “long delayed” but “very appropriate”.
“I have moments of joyous tears,” Ms Robson said. “I’m just flabbergasted that something finally broke and somebody is finally holding accountability.
“This is why King Charles is King. He is showing the world, including America, what it looks like to have somebody held accountable.”