Approached by a journalist at Geneva Airport, she declined to discuss the Duke’s legal case, but said: “Onwards and upwards.”

It came as a former school friend of Ms Giuffre, who gave evidence at Ghislaine Maxwell’s trial, recalled Ms Giuffre telling her of a night with the prince in the first contemporaneous account of the meeting.

Carolyn Andriano told the Daily Mail that Ms Giuffre, then Miss Roberts, texted her from London in March 2001 to say she was going for dinner with Prince Andrew, Maxwell and Epstein.

Ms Andriano, who waived her anonymity for the interview, said: “I asked her if she’d been to the palace. And she said ‘I got to sleep with him’. I said ‘What? You’re f****** with me’ and she said ‘no, I got to sleep with him’. She didn’t seem upset about it. She thought it was pretty cool.”

Debate over possible settlement rages on

The Duke has so far indicated that he wants to fight the allegations and clear his name.

However, if he does opt to offer Ms Giuffre a payoff, which is likely to exceed £5 million, the Queen would be asked to contribute, alongside his own input, The Telegraph understands.

However, any potential deal would include a “no admission of fault or liability” clause as well as a non-disclosure agreement, preventing either party from discussing the settlement or the case in public, sources suggest.

The settlement issue has gathered traction in recent days as the Duke awaits a critical ruling from Judge Lewis Kaplan on his motion to have the civil case dismissed.

Andrew Brettler, his lawyer, argued that Ms Giuffre had “waived her rights” to sue him when she entered into a $500,000 (£370,000) release agreement with Epstein in 2009.

However, Judge Kaplan rejected most of Mr Brettler’s points and legal experts said it appeared “unlikely” that he would find in the Duke’s favour.