Pressure was mounting on Prince Andrew last night to answer questions about his paedophile friend Jeffrey Epstein.

Young victims of Epstein begged the Duke of York to help them get justice as the prince was offered the opportunity to give sworn testimony on 'everything he knows'.

After the duke declared himself 'appalled' at reports of the US financier's sex abuse of teenage girls, he was offered the chance to stand by his word and help their cases.

Notorious: The picture of Prince Andrew and Virginia Roberts. She claims it was taken in London in 2001. After the duke declared himself 'appalled' at reports of the US financier's sex abuse of teenage girls, he was offered the chance to stand by his word and help their cases

Lawyers said they looked forward to sitting down with Prince Andrew 'as soon as possible', suggesting that he go on the record about Epstein, whom he once reportedly vowed to 'be loyal' to.

Today it can be revealed that flight logs, obtained by the Daily Mail, show that one of Epstein's victims, 'sex-slave' Virginia Roberts, was flown to London, New York and the Caribbean in 2001.

She has claimed that as a 17-year-old she met the duke in all three places and, in each case, research by the Mail suggests the duke was in the same vicinity at the same time.

Today it can be revealed that flight logs (pictured), obtained by the Daily Mail, show that one of Epstein's victims, 'sex-slave' Virginia Roberts, was flown to London, New York and the Caribbean in 2001

Yesterday Buckingham Palace refused to answer a series of questions concerning when and where the duke had spent time with Epstein and Miss Roberts.

There is no suggestion the flight logs support the allegation made by Miss Roberts that Epstein 'forced' her to have sex with the duke in those locations and nor does it undermine his repeated and emphatic denials of 'any sexual contact or relationship' with Miss Roberts.

Her allegations against him, initially made in court documents, were thrown out by an American judge who ordered them struck out as 'immaterial and impertinent'.

But last night, Brad Edwards, a lawyer representing Miss Roberts and others, said the duke might have useful information about Epstein's sex-trafficking operation.

Andrew was introduced to Epstein in the 1990s and remained a friend even after the financier served a 13-month sentence for having sex with underage girls and became a registered sex offender.

He flew on Epstein's private plane at least three times and stayed at the billionaire's New York mansion in 2010 where he was photographed waving to a woman out of the front door.

When those photos were published over the weekend, the duke issued a statement via Buckingham Palace. It said: 'The Duke of York has been appalled by the recent reports of Jeffrey Epstein's alleged crimes.

When photos were published over the weekend, the duke issued a statement via Buckingham Palace. It said: 'The Duke of York has been appalled by the recent reports of Jeffrey Epstein's alleged crimes'

'His Royal Highness deplores the exploitation of any human being and the suggestion he would condone, participate in or encourage any such behaviour is abhorrent.'

In response, Mr Edwards told the Daily Mail: 'It sounds like he is willing to fully co-operate as we, on behalf of Jeffrey Epstein's victims, continue to investigate.

'For that we are very pleased. I would like to personally help him provide these victims his assistance. I look forward to co-ordinating a formal deposition where he will be given the opportunity to tell us everything he knows.'

The Mail's flight logs investigation comes as Prince Andrew's efforts to distance himself from the scandal were plunged into turmoil as it emerged he had hosted the disgraced US financier and his entourage at Balmoral.

The Mail's flight logs investigation comes as Prince Andrew's efforts to distance himself from the scandal were plunged into turmoil as it emerged he had hosted the disgraced US financier and his entourage at Balmoral (pictured)

The headache for Andrew intensified as a 2011 article in Vanity Fair resurfaced in which a friend talked about trying to persuade him to stay away from Epstein.

A source told the magazine that they begged Andrew to cut Epstein off but the duke allegedly replied: 'Stop giving me a hard time. You're such a puritan.'

The conversation 'descended into a screaming match' before Andrew said: 'Leave me alone. Jeffrey's my friend. Being loyal to your friends is a virtue. And I'm going to be loyal to him,' it was claimed.

The woman who stayed at Balmoral spent almost a year in Epstein's orbit, joining him on about a dozen trips. Epstein (above) gave her a place to live in New York, rent-free, and later paid for her to go to college

Miss Roberts first landed her claim that she was a schoolgirl 'sex slave' in a US court in 2014. She claims she was forced to submit to abuse by rich and powerful men, all of whom deny wrongdoing.

Last night Buckingham Palace said: 'This relates to proceedings in the United States, to which The Duke of York is not a party. Any suggestion of impropriety with underage minors is categorically untrue. It is emphatically denied that The Duke of York had any form of sexual contact or relationship with Virginia Roberts. Any claim to the contrary is false and without foundation.'

Miss Roberts claims she had been groomed for abuse since 15 by billionaire Epstein – said to be 'addicted' to molesting children – and his 'madame' Ghislaine Maxwell, the daughter of disgraced tycoon Robert Maxwell.

Legal papers filed in Palm Beach, Florida, alleged that an underage Miss Roberts 'was forced to have sexual relations' with Andrew 'in three separate geographical locations: in London (at Ghislaine Maxwell's apartment), in New York, and on Epstein's private island in the US Virgin Islands.'

There has been no claim that Andrew was aware that Miss Roberts was acting under duress and he denies any such incidents happened at all.

The flight logs for Epstein's luxury black Gulfstream jet are not publicly available 'at the request of the owner', but the Mail has obtained entries for March and April 2001, showing Miss Roberts being flown on a six-day whirlwind tour from Palm Beach to Canada, Paris, Grenada in Spain, Tangier in Morocco, and finally touching down at London's Luton airport on March 9.

The flight logs for Epstein's luxury black Gulfstream jet (pictured) are not publicly available 'at the request of the owner', but the Mail has obtained entries for March and April 2001, showing Miss Roberts being flown on a six-day whirlwind tour from Palm Beach to Canada, Paris, Grenada in Spain, Tangier in Morocco, and finally touching down at London's Luton airport on March 9

There is nothing in the Court Circular about the duke's whereabouts, but Miss Roberts claims this was when the now-notorious photo was taken of herself with him at Miss Maxwell's London apartment. A month later, on Monday April 9, the duke began an official visit to the US in his capacity as chairman of the trustees of the Outward Bound Trust.

That day's Court Circular states he departed 'this morning' from London's Heathrow Airport, arriving in New York later that day. As it was an official trip, the flight was funded by British taxpayers.

The same day, Miss Roberts also flew to New York. She and Epstein left his £8million mansion in Palm Beach, Florida, and the flight log shows they flew aboard his 22-seat Gulfstream –with its personalised licence code ending 'JE' – to New York via Atlantic City.

Although Miss Roberts and the duke were both in New York, there is no information to suggest whether they met, and the Palace has declined to comment, beyond denying they had any 'relationship'.

The next morning, a Tuesday, the Duke flew to Boston for a series of royal engagements. According to Miss Roberts' claims in newspaper interviews, it was around this time – Easter – that she was ordered to Epstein's mansion in New York and met Andrew again.

Yesterday the Palace was specifically asked if he met Miss Roberts at this time, and it declined to answer, other than to say he denies any sexual encounters with her.

The next meeting she recounts was in the Caribbean. The flight logs show that Miss Roberts and Epstein left New York on April 11 aboard the jet for St Thomas, in the US Virgin Islands, for a boat transfer to Epstein's private island next door.

The Court Circular does not state the duke's whereabouts for the next few days, but it appears he too flew south – because by Easter Sunday, April 15, he was reportedly 'in the Bahamas'. He had been absent from the Queen's Easter service at Windsor Castle, and a royal courtier explained to the Daily Telegraph, which published the titbit, that he was on holiday in the Bahamas with ex-wife Sarah Ferguson and their daughters.

It is unknown when the duke arrived in the Bahamas – about a two-hour flight from Epstein's island – or when he left. Yesterday the Mail asked Buckingham Palace whether Andrew stopped at Epstein's island en-route to the Bahamas. A spokesman again declined to confirm or deny the suggestion.

According to Miss Roberts' claims, the duke was there for one night. She claimed she flew to the island with Epstein and Miss Maxwell – which is confirmed by the flight logs. The Mail asked the palace a series of questions about Prince Andrew's movements that week but none of them were answered.

Miss Maxwell has strongly denied the allegations against her as salacious, spurious and untrue. Epstein, 66, hanged himself in his cell earlier this month.