Buckingham Palace tonight furiously denied allegations that Prince Andrew flew repeatedly with Jeffrey Epstein and his 'sex slave' Virginia Roberts, saying they were demonstrably untrue.

The claims, made in court documents by Epstein's former pilot, place the Duke of York on the billionaire's private jet with Roberts on at least four occasions in April and July 2001.

But a spokesman for the palace dismissed the claims, pointing out the testimony 'does not stand up to scrutiny' and that Andrew was undertaking official engagements a continent away from Epstein on some of the dates in question.

The notorious picture of Prince Andrew, Virginia Roberts and Ghislaine Maxwell, allegedly taken in London in 2001

Epstein's pilot said the Prince boarded a flight from Teterboro, New Jersey on April 11, 2001. On that day he was in the U.S., visiting a Outward Bound centre in Boston, before flying back to New York

The allegations were made in a 2016 deposition given by Epstein's former pilot David Rodgers, in relation to Virginia Roberts' lawsuit against Ghislaine Maxwell - Epstein's longtime associate and alleged procurer of underage girls. Maxwell denies any such allegations.

On April 11 2001 Rodgers flew Epstein's Gulfstream from Teterboro airport in New Jersey to the Caribbean island of St Thomas, near the British Virgin Islands. Epstein's private island of Little St James lies just off the coast of St Thomas.

According to the passenger manifest, handwritten by Rogders in 2001, aboard the jet that day were 'JE, GM, AP, BK, VR, Joann'.

In the deposition, for which the pilot was reading from his own 2001 flight logs, the pilot was asked: 'On that flight, Jeffrey Epstein, Ghislaine Maxwell, Prince Andrew, Banu [Küçükköylü], Virginia Roberts and Johanna?'

He replied: 'Yes'.

'AP' is listed as a passenger alongside Roberts and Epstein on at least three other occasions: April 16, July 4, and July 8.

But elsewhere in Rodgers' own notes it appears 'AP' does not refer to the Prince, as an 'AP' is listed alongside 'Prince Andrew' and 'Bodyguard' on May 12, 2000.

And the court circular shows Andrew was in the UK on July 4, when Rodgers claims he was on board Epstein's jet on a trip from St Thomas to Florida.

In his interview, Rodgers said Prince Andrew was on at least three flights, on April 11, July 4 and July 8 (pictured in the flight logs), but Buckingham Palace points to the court circular which shows he carried out duties in Boston in April and was in Lancashire in July

In his 2016 deposition Rodgers is reading from his handwritten 2001 passenger manifests, and says Prince Andrew was a passenger where 'AP' is recorded on his logs. But elsewhere (above) an 'AP' is listed by Rodgers alongside 'PRINCE ANDREW' on the same flight in May of 2000

When photos of Andrew at Epstein's New York mansion, above, were published over the weekend, Buckingham Palace issued a statement saying 'The Duke of York has been appalled by the recent reports of Jeffrey Epstein's alleged crimes'

Rodgers had previously used the initials AP for Epstein's designer Alberto Pinto, and 'AP' may also have been used for Epstein's chef, Adam Perry Lang.

Flights Prince Andrew is said to have taken vs His royal engagements According to David Rodgers testimony, Prince Andrew was on at least three flights with Epstein: - Flight 1: April 11, 2001: Flight from Teterboro Airport, New Jersey to St Thomas, in the U.S. Virgin Islands. The party are said to have returned on April 16. - According to the online court circular archive, the Prince was in the U.S. on that date and carried out a visit to the Willauer School in Boston, Massachusetts before returning to New York. No other date is given in the court circular for the Duke of York until he arrives in Korea on April 19. - Flight 2: July 4, 2001: Flight from St Thomas, in the U.S. Virgin Islands to Palm Beach, Florida. - The court circular archive states that on July 4th, the Prince visited St. Luke's Secondary School in Southsea before opening an exhibition at the Portsmouth Historic Dockyard. He later visited the Queen Alexandra Hospital, Portsmouth. - Flight 3: July 8, 2001: Flight from Palm Beach, Florida to Teterboro Airport, New Jersey. - The court circular does not have any engagements listed for the Prince on this date, although two days later he visited Burnley, Lancashire. Advertisement

Tonight a spokesman for Buckingham Palace said: 'This evidence statement was submitted in a case in which the Duke was not a party and in which any suggestion of impropriety with underage minors is categorically untrue.

'The testimony does not stand up to scrutiny and is inconsistent when checked against the court circular. It places the Duke in different places at the same time and in some cases on different continents.

'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.'

There is no suggestion the flight logs or the deposition 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'.

Billionaire Epstein, 66, hanged himself in jail in New York on August 10.

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 is understood to have flown 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.

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 2001