Paedophile billionaire Epstein’s former slave Virginia Roberts revealed the account in 2,000 pages of legal documents released hours before his death.
Epstein – a powerful financier with many influential friends – is believed to have taken his own life as he faced 45 years in prison accused of running a sex trafficking empire.
The Queen’s second son Prince Andrew is known to have been pals with Epstein, and has previously come under scrutiny over their friendship.
Documents filed include three alleged sexual encounters between Virginia and the Duke of York.
Buckingham Palace has firmly denied any “impropriety with underage minors”.
“I would just giggle not really knowing how to reply to an aging man with a bad smile”
Virginia says her account is “99 per cent true” but her own lawyers have described it as “fictionalised”.
Andrew strenuously denies any sexual contact with Virginia, who says she was 17 at the time.
The Duke of York is currently on holiday with his ex-wife Sarah Ferguson and the Queen in Balmoral.
Questions has been raised in the US of how Epstein could kill himself when he had days ago been on suicide watch.
Virginia claims she first met the royal dad of two on a trip to London in 2001 when she was 17.
Epstein and his British socialite ex-lover Ghislaine Maxwell were also there.
She claims Andrew guessed her age.
The sex slave said he then showed her his “terrible pelvic smashing” dance moves at the nightclub Tramp in London.
Virginia wrote: “Moving his hands across the curves of my body, he was whispering sweet nothings into my ear and kissing my neck.
“I would just giggle not really knowing how to reply to an aging man with a bad smile.”
Virginia claims they then went back to Maxwell’s house, and she claims her and Prince Andrew had a bath.
“He was adorning my young body, particularly my feet, caressing my toes and licking my arches,” she wrote.
Virginia then claims they “retired to my bedchamber for the longest ten minutes of my life”.
She claims the second encounter was months later in New York.
And she added the third was on Epstein’s private island in the Caribbean.
The paper, from 2011, was released by a New York court from a defamation case between Ms Maxwell and Virginia, who is now 35 and a mum of three.
In a statement, 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 had any form of sexual contact or relationship with Virginia Roberts.
“Any claim to the contrary is false and without foundation.”