Prince Andrew
Prince Andrew has strenuously denied claims he had sex with an underage sex slave Reuters

Prince Andrew allegedly licked the toes of 'sex slave' Virginia Roberts and showered her with compliments, diary extracts published in the United States claim.

Roberts purports the Duke of York played a guessing game with alleged madam Ghislaine Maxwell over how old Roberts was, before he had sex with the 17-year-old.

In diary extracts published by US outlet Radar Online, Roberts writes the prince "was caressing every part of my naked body and filling my head with endless compliments about my blossoming figure.

"When his climax was achieved, he was not the same attentive guy I had know for the last few hours.

"Instead, [he] quickly got dressed, said his goodbyes and slipped out of my bedroom to the driver still waiting for him outside," she added.

One graphic detail described how the Duke, the second son of the Queen and the Duke of Edinburgh, licked her toes in a bathtub after returning from a club.

The revelations come after documents were submitted to a court regarding a legal battle between US prosecutors and convicted sex offender, and former acquaintance of the prince, Jeffrey Epstein and girls he allegedly sexually exploited.

It is claimed multi-millionaire Epstein sexually exploited Roberts between 1999 and 2002. She claims that she was 17 when she had sex with the prince, which in the state of Florida, where the court papers were lodged, means she was a minor.

Epstein was sentenced to 18 months imprison after pleading guilty to soliciting sex from a 14-year-old girl at his Florida mansion in 2008.

Prince Andrew, Jeffrey Esptein and Ghislaine Maxwell have all repeatedly denied the allegations.

Elsewhere in the extracts, Roberts recalled going to a club with the Duke, with his dancing apparently sticking in her mind.

"He was the most incredibly hideous dancer I had ever seen, not to mention how embarrassing it was to have to be the one he was smashing pelvics with, even if he was a prince,'' she recalled.