Prince Andrew has agreed to speak publicly for the first time about his friendship with the child sex offender Jeffrey Epstein, in a “no holds barred” interview with the BBC’s Newsnight programme to be broadcast on Saturday night.

The prince has been the subject of fierce speculation over his relationship with the financier, who was found dead in a New York jail cell three months ago.

Epstein’s accuser Virginia Giuffre claims Prince Andrew was “an abuser, a participant” in her exploitation as a teenager and says she was coerced to have sex with him.

The prince has previously strongly denied any inappropriate behaviour or being aware of any such behaviour by Epstein, but he has struggled to stop the flow of damaging claims. Newly released footage showed him at Epstein’s home in 2011 after the financier was released from a spell in jail.

Newsnight sources said the interview was a result of six months of negotiations with the royal household, with an agreement that there would not be any advance vetting of the questions.

The interview was conducted on Thursday at Buckingham Palace and the BBC has decided to broadcast a special hour-long edition of the show at 9pm on Saturday. It was conducted by the lead Newsnight presenter, Emily Maitlis, who promised it would be “no holds barred”.

The palace has until now relied on issuing strongly worded press statements, while some newspapers have reported “sources close to Prince Andrew” as saying that a photo of him with Giuffre was fake because his fingers were “much chubbier” in real life.

Giuffre claims she was made to have sex with Andrew in 2001 when she was 17 after being flown to London on a private jet. She has previously said that while he denies the claims, “he knows the truth and I know the truth”.

• This article was amended on 18 November 2019 to correct a description of Epstein’s offending.