The Duke of York has been dealt a major blow after a sponsor of his flagship business project said it was not renewing support – as calls continued for him to make a statement about Jeffrey Epstein.

Andrew is facing the embarrassing prospect of charities and institutions he is associated with distancing themselves, as lawyers for the convicted sex offender’s victims urged him to tell US authorities what he knows.

The duke was caught up in further controversy when a newspaper columnist claimed Andrew used a racially-offensive word during a Buckingham Palace meeting in 2012.

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The Queen and other senior royals are said to “back and believe” Andrew’s defence of himself in the BBC interview “100%”, sources told the Evening Standard.

One alleged Epstein victim gave an emotional account of her ordeal as she launched a civil lawsuit against the sex offender’s estate and made a direct appeal to the duke after her lawyer, Gloria Allred, called on him to make a statement.

The 31-year-old – known only as Jane Doe 15 – said: “I would also like to say I agree with Gloria that Prince Andrew, and any others that are close to Epstein, should come forward and give a statement under oath on what information they have.”

The fall-out from Andrew’s Newsnight appearance has already begun, with the Outward Bound Trust, which the duke supports as patron, saying it will hold a board meeting in the next few days when members will discuss issues raised by Saturday’s interview.

The student jury at Huddersfield University, where Andrew is chancellor, passed a motion to lobby the duke to resign, with a full statement expected from the Students’ Union on Tuesday.

KPMG’s sponsorship contract with Andrew’s Pitch@Palace, a mentoring scheme for tech start-ups and entrepreneurs, expired at the end of October and will not be renewed, a source told the PA news agency.

A spokesman for Buckingham Palace said: “KPMG’s contract with Pitch@Palace ended at the end of October. A full programme of Pitch@Palace events is continuing across the United Kingdom.”

Pharmaceutical giant AstraZeneca told the Daily Telegraph it is also reviewing its future with the mentoring scheme: “Our three-year partnership with Pitch@Palace is due to expire at the end of this year and is currently being reviewed.”

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Andrew’s appearance on Newsnight to explain his friendship with the convicted sex offender and deny allegations of having sex with an under-age teenager has been widely condemned, but the duke is said to being standing by his decision to put his side of the story.

The Queen, pictured with her son AndrewThe Queen reportedly gave the green light for the Duke of York’s television interview (Victoria Jones/PA)

US lawyer Spencer Kuvin, who represents a woman who claims she was a victim of Epstein, told BBC Radio 4’s Today programme that Andrew should come forward to help the ongoing investigation into the disgraced American financier.

Prime Minister Boris Johnson was asked if he would encourage Andrew to co-operate with US authorities about his knowledge of the disgraced financier’s activities but he brushed the question off, during an election campaign event at the CBI annual conference, saying “nice try there”.

It also emerged on Monday that Virginia Giuffre has given an interview to BBC’s Panorama.

PA understands that the 35-year-old reiterated her claims that she slept with Andrew when she was just 17 after being trafficked by Epstein.

The interview, which was filmed three weeks ago, is due to be broadcast in the coming weeks.

A spokesman for the BBC said: “We never comment on investigations.”

The duke’s interview on Saturday has been widely criticised, with commentators questioning his responses and condemning his unsympathetic tone and seeming lack of remorse over the friendship with Epstein, who killed himself in jail while facing sex trafficking charges.

The Evening Standard published on its front page the claim made by its columnist Rohan Silva that, while a Downing Street aide specialising in the tech economy, the duke made a racist remark.

He told the newspaper that, when he asked Andrew if the government department responsible for trade “could be doing a better job”, the duke replied: “Well, if you’ll pardon the expression, that really is the n***** in the woodpile.”

Sources have categorically denied that Andrew used the word.

During the interview, the duke, questioned by Newsnight presenter Emily Maitlis, twice stated that his relationship with Epstein had some “seriously beneficial outcomes”, giving him the opportunity to meet people and prepare for a future role as a trade envoy.

Andrew denied that he slept with Virginia Giuffre, one of Epstein’s victims, on three separate occasions, twice while she was under age, saying one encounter in 2001 did not happen as he spent the day with his daughter, Princess Beatrice, taking her to Pizza Express in Woking for a party.

The same alleged sexual liaison, which the American said began with the duke sweating heavily as they danced at London nightclub Tramp, was factually wrong as Andrew said he had a medical condition at the time which meant he did not sweat.