Buckingham Palace has risked reigniting the controversy surrounding Prince Andrew by announcing he will continue his work with a business mentoring initiative, a day after he said he was stepping down from public duties.

The Duke of York will continue to be involved with Pitch@Palace, which has held events at Buckingham and St James’s palaces, “but will look at how he takes this forward outside of his public duties, and outside of the palace”, a statement said.

“Naturally there will be a transition period while this takes place,” Buckingham Palace said.

The decision to retain Prince Andrew’s links to the initiative, which corporate partners such as BT have abandoned in recent days, raised concerns that it muddied the waters of what had appeared to be a clean break from royal duties.

Sources at one backer of the prince’s initiatives with the business community called for clarity. “To put it bluntly, this situation can’t last – the in-out-in-out hokey-cokey can’t last. So I would like to see some clarity on [his continuing involvement].”

The decision signals a desire on the part of the palace to protect what was seen by some as a successful scheme. At least one backer had suggested to the Guardian that Andrew could make way for another royal, such as Prince Harry or William.

A spotlight also fell on the Prince Andrew Charitable Trust, which holds a controlling stake in the Pitch@Palace initiative. Charity Commission filings show the trust spent approximately £40,000 on charitable activities and £1.24m on raising funds in the 2017-18 financial year. Andrew is not listed as a trustee on the four-person board, which includes his private secretary, Amanda Thirsk.

Graham Smith, the chief executive of the campaign group Republic, said: “It’s not a surprise, given that royal charities we have looked into have similar patterns of minimal spending on charitable activities and quite a lot on fundraising, but it does appear to be a vanity project for Prince Andrew and a way giving him something to do. The trust is obliged to take independent decisions, irrespective of whether it has his name on it.”

Huddersfield University announced on Thursday that the prince had stood down as chancellor after a student panel called for his resignation. On Thursday night, the students’ union at London Metropolitan University said they would be lobbying for his removal as its patron.

On Wednesday in his statement saying he was standing down from public duties, the prince said he was willing to help “any appropriate law enforcement agency” with their investigations after what he accepted was his “ill-judged association” with Jeffrey Epstein.

Lisa Bloom, a lawyer representing five of Epstein’s victims, demanded further action by the prince. In a tweet she called on him and his staff to appear for civil depositions and produce all relevant documents about his contact with Epstein.

I've been working with my 5 Epstein victim clients for months. Prince Andrew was simply not credible in his interview. He and his staff must cooperate with all investigations, show up for civil depositions and trials, and produce all documents. We are just getting started. https://t.co/7IFImNRfj5 — Lisa Bloom (@LisaBloom) November 21, 2019

Later, when asked by BBC Radio 4’s Today programme whether she would approach Prince Andrew to serve him with a subpoena to provide a legal statement about his time with Epstein, Bloom replied: “We may as part of our investigation.”

She added: “It may be difficult to serve a deposition subpoena on him. But we believe that nobody is above the law, and that everybody should have to answer questions, if they have relevant information, and he clearly does have relevant information.

Profile Who was Jeffrey Epstein? Show Born in Brooklyn in 1953, Jeffrey Epstein was a convicted sex offender and financier who died in jail in August 2019 while awaiting trial for the sex trafficking of minors in Florida and New York. He had previously served 13 months in jail after being convicted in 2008 of procuring an underage girl for prostitution and of soliciting a prostitute. A medical examiner declared Epstein's death a suicide. His death came after unsealed documents in New York revealed the extent of his abuse of young women at his home in Palm Beach, New York and the Virgin Islands. An earlier attempt to prosecute him on similar charges had collapsed when authorities granted him an unusually generous deal to plead guilty to state prostitution charges in Florida.

Epstein made his name at the investment bank Bear Stearns before opening his own firm in 1982, managing money for clients with wealth in excess of $1bn. The business came with an intensive social schedule. Epstein positioned himself as a party figure in Manhattan and Palm Beach, Florida, and courted the rich, famous and powerful across America and the world.

Epstein’s circle of friends and acquaintances has included Donald Trump; Bill Clinton; Prince Andrew; Leslie Wexner, founder of the company that owns the Victoria’s Secret lingerie brand; and many other prominent names in law, entertainment and politics. In July 2020, his long-term confidante and personal assistant Ghislaine Maxwell was arrested by the FBI on charges related to Epstein's sex crimes. Photograph: New York State Sex Offender Registry

It is understood there have been discussions within the royal family about the situation, with Prince Andrew talking to the Queen and the Prince of Wales.

Andrew met the Queen at Buckingham Palace on Wednesday before his decision to step down was announced.