The woman who alleges that she was made to have sex with Prince Andrew when she was 17 has told a US court that she believes video footage exists of her having underage sex with powerful associates of Andrew’s friend Jeffrey Epstein.

Virginia Roberts also alleged in a new affidavit filed on Friday that she was so badly assaulted by Epstein’s friends that she thought she might die.

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“There were times when I was physically abused to the point that I remember fearfully thinking that I didn’t know whether I was going to survive,” she said.

Related: Modelling scout to take legal action over claims linking him to Jeffrey Epstein

Now 31, Roberts alleged in a court filing in December that she was repeatedly forced to have sexual relations with Andrew by Epstein, a wealthy former investment banker and hedge fund boss who was jailed in Florida in 2008 for sex offences. Andrew and Buckingham Palace vehemently deny Roberts’s claim, which they say is totally without foundation.

Roberts claimed on Friday that US authorities were holding back damning evidence of activities that she was made to engage in while working as Epstein’s so-called “sex slave”. She said she was the victim of a “major cover-up”.

“Based on my knowledge of Epstein and his organisation, as well as discussions with the FBI, it is my belief that federal prosecutors likely possess videotapes and photographic images of me as an underage girl having sex with Epstein and some of his powerful friends,” she said.

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Despite an inquiry by the FBI turning up dozens of alleged victims of Epstein’s underage sex abuse, he secured a deal that saw him serve 13 months in jail in return for pleading guilty to soliciting prostitution from a minor. The deal has been criticised by some of his alleged victims as unusually lenient.

Roberts is seeking to join a long-running lawsuit against the US government filed by other alleged victims of Epstein to a federal court in Florida. The women claim that Epstein’s plea deal violated their constitutional rights, and that his powerful allies – including presidents, influential lawyers and other celebrities – may have helped win him special treatment.

Dismissed as a liar and a fantasist by Epstein allies, Roberts filed with her affidavit on Friday previously undisclosed receipts for a flight from New York to Thailand in September 2002 and a stay costing several thousand dollars at the Royal Princess hotel in Chiang Mai. All the bills appeared to have been paid for by “J Epstein”.

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Roberts, who says she was recruited for Epstein at 15, has previously alleged that she was sent on the Thailand trip by Epstein to learn Thai massage and interview a Thai girl “to bring back to the United States” for him. Instead, she says, she met a man whom she married and fled with him to Australia for more than a decade.

Government prosecutors say that Roberts was properly notified about the plea deal at the time it was struck and has waited too long to join the lawsuit. Roberts argues that she did not fully understand the letter sent to her by prosecutors and was too scared of repercussions from Epstein’s powerful friends to come out of hiding.

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Roberts was contacted and interviewed by FBI agents at the US consulate in Sydney soon after first going public with allegations against Epstein and Andrew in a 2011 interview with the Mail on Sunday. However, she wrote, “they seemed like they were being blocked from doing what they wanted to do – which I thought was to arrest Epstein and his powerful friends for all of their illegal sexual crimes.”

Roberts went on in her affidavit on Friday to allege that authorities already hold evidence “that will support what I have been saying about Epstein and his associates”, including the video and photographic material. She said she did not understand why no action had been taken.

“I have asked the FBI to show me the video surveillance and other pictures of me that I believe they have in their possession,” she said. “They said that I would have to go to the prosecutors to get them. But the prosecutors will not share anything with me.”

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She also claimed: “There are also many people who could confirm what I am saying. I hope that these people will come forward and tell the truth.”

Roberts is referred to in the court documents as Jane Doe 3. Pleadingwith Judge Kenneth Marra to allow her to join the lawsuit brought byJane Does 1 and 2, Roberts made increasingly serious allegations about her treatment at the hands of some of Epstein’s friends, while not naming any other alleged abusers.

Noting that she had already disclosed the identities of some powerful Epstein allies with whom she was made to have sex, Roberts wrote: “There were others, though, who I continue to refrain from naming publicly out of fear for physical repercussions.”

Related: Jeffrey Epstein: inside the decade of scandal entangling Prince Andrew

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The 31-year-old said her anxiety about possibly being in danger was partly fuelled by memories of the physical abuse she suffered from some of Epstein’s friends, while again not specifying any by name. Roberts has long claimed that Epstein “debriefed” her after she had sex with his allies so that he would possess intimate and potentially embarrassing information that could be used for blackmail.

“Jeffrey Epstein knew about this physical and sexual abuse because I would detail it for him as part of my debriefing,” she said. “Epstein didn’t care. Epstein said things like, ‘You get that sometimes.’ I told him how much I hated having to be with some people, but Epstein still sent me back. I had no choice.”

Epstein dismissed the allegations against him last month, in his first formal remarks on the revived scandal. Condemning the “media frenzy” surrounding his case , Epstein said in a court filing said that he and his associates “have been the subject of the most outlandish and offensive attacks, allegations, and plain inventions”.

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