Buckingham Palace officials have scrambled to quell the growing crisis engulfing Prince Andrew after claims in an American court case that he had “sexual relations” with an underage girl who had been forced into sexual slavery by the multi-millionaire investor Jeffrey Epstein.

The Duke of York returned to Windsor from a new year holiday in the Swiss ski resort of Verbier to face what courtiers described as “lurid and deeply personal” claims detailing his alleged relations over a decade ago with Virginia Roberts.

US court papers filed last week alleged that Roberts, described using the alias Jane Doe #3, was forced to have “sexual relations” with Prince Andrew in London, New York and on Epstein’s private island in the US Virgin Islands during an alleged orgy with other underage girls.

British newspapers published earlier interviews with Roberts in which she claimed to detail her alleged encounters with Prince Andrew.

The Guardian was aware of Roberts’s identity on Thursday but decided not to name her out of respect for her wish to bring the case anonymously.

However, over the weekend she was named by and pictured in several newspapers, and was subsequently named by Buckingham Palace. The Guardian approached her lawyers on Sunday before naming her.

The court papers were filed by Roberts’s lawyers to a district court in Florida as part of a case against the US government over a plea bargain it struck with Epstein. They said Epstein instructed her “to give the prince whatever he demanded and required [her] to report back to him on the details of the sexual abuse”.

Aides stepped up a highly unusual royal operation launched on Saturday to categorically deny the claims. Prince Andrew personally decided to issue a strong denial while still in Verbier.

He approved a statement, extraordinary in its frankness for a member of the royal family, which vehemently denied “any form of sexual contact or relationship with Virginia Roberts” and added: “The allegations made are false and without any foundation.”

In an attempt to stem the flow of sordid allegations Buckingham Palace on Sunday wrote to editors reminding them of their responsibilities under the Independent Press Standards Organisation code and the law. Palace lawyers were also said to be closely reviewing coverage and “assessing the legal position in respect of Sunday’s newspapers”.

Prince Andrew’s friendship with Epstein, once known as one of America’s richest financiers, was first questioned in 2007 when it emerged that the FBI had begun an investigation into claims Epstein was paying underage girls for sex. Then in 2008 a federal inquiry was dropped after Epstein negotiated a deal with prosecutors in which he agreed to plead guilty to soliciting paid sex with a minor. He served 13 months of an 18-month sentence and is now a registered sex offender. Many of his alleged victims have since reached out-of-court settlements with Epstein.

Prince Andrew and Jeffrey Epstein (right) pictured together in New York’s Central Park. Photograph: Jae Donnelly

The latest court papers seek disclosure of any documents that may suggest that Prince Andrew, along with the Harvard Law School professor Alan Dershowitz, lobbied the US government to give Epstein a more favourable plea deal and a non-prosecution agreement.

Buckingham Palace issued a strenuous denial stating: “The Duke of York would not and did not interfere in an active case.” Dershowitz has also denied the claim.

The Guardian understands the plea deal states: “If Epstein successfully fulfils all the terms of this agreement, the United States also agrees that it will not institute any criminal charges against any potential co-conspirators of Epstein including but not limited to [four named individuals not including Prince Andrew or Dershowitz].”

It could mean that if Prince Andrew is ever considered a “co-conspirator” with Epstein, he could be prevented from facing criminal charges.

On Sunday the Duke went straight to his home at the Royal Lodge at Windsor Castle and is expected to maintain a low profile in the coming days, although he is not understood to have cancelled any events.

The Queen is set to remain in Sandringham, scotching reports of face-to-face crisis talks as soon as her son arrived in the UK.

Palace aides said that despite the allegations Prince Andrew planned to continue his work promoting vocational education, technology and enterprise.

Explaining Prince Andrew’s decision to breach royal convention and directly tackle allegations about his private life, an aide said: “When there are lurid and deeply personal allegations made against you to a national newspaper that are directly linked to a civil case in which you are accused of having sexual relations with underage minors, the natural instinct is to come out and say it is not true.

“The Duke did not want these claims to go uncontested. Commenting on a member of the royal family’s private life or commenting an ongoing legal case goes against what the palace would do typically.

“The default position is no comment but these are extraordinary circumstances and given the allegations filed in court and coming from the Sunday papers, the decision was taken that it was time to issue a denial on the record.”

According to Roberts’s court filing, Dershowitz is also accused of having sexual relations with her “on numerous occasions while she was a minor, not only in Florida, but on private planes, in New York, New Mexico and the US Virgin Islands”.

On Saturday he told the BBC’s Today programme: “The story is totally made up.”

He claimed: “She’s lied about other public figures including a former prime minister and others who she claims to have participated in sexual activities with, so I think it must be presumed all her allegations against Prince Andrew were false as well.”

Dershowitz told the Guardian: “I will fight this to the very end. I want the facts to come out.”

He said he did not believe the language in Epstein’s plea deal, barring criminal charges against “any potential co-conspirators”, would necessarily give him immunity from prosecution.

However, in the event that the promise not to prosecute co-conspirators did apply to him, Dershowitz insisted he would “waive any possibly immunity” to clear his name.

Dershowitz said his lawyers would submit a sworn affidavit to both the Florida court and the judicial bar on Monday, categorically denying sexual relations with any minors, accusing Roberts of making up the story.

Roberts declined to comment on Sunday. But in a statement released through her lawyers last week, she said: “These types of aggressive attacks on me are exactly the reason why sexual abuse victims typically remain silent and the reason why I did for a long time. That trend should change. I’m not going to be bullied back into silence.”