In August, as other accusers stepped forward, she said of the prince, “He knows exactly what he’s done, and I hope he comes clean about it.”

In his interview, the duke cast doubt on several accusations. For example, in explaining the photograph that appeared to show him with Ms. Giuffre, he stopped short of saying the picture had been doctored, as some of his friends have suggested. But he said that he never dresses casually when in London, that he avoids public displays of affection with strangers and that he could not have been at the place the photograph was taken.

“The photograph was taken upstairs,” Prince Andrew said, “and I don’t believe I ever went upstairs.”

Perhaps even more damaging was his explanation about why he stayed with Mr. Epstein at his Manhattan mansion in 2010, after his host was released from prison. It was “convenient,” the prince said, though he insisted that he had made the visit solely to break off their relationship.

As for a photograph of Prince Andrew, now 59, walking with Mr. Epstein in Central Park that was published in The Daily Mail in August, renewing questions about the propriety of their association, the duke said with a wan smile: “That’s the bit that, as it were, I kick myself for on a daily basis because it was not something that was becoming of a member of the royal family.”

“We try and uphold the highest standards and practices,” he added, “and I let the side down, as simple as that.”

Even after all the lurid details of Mr. Epstein’s trafficking in underage girls emerged in court, Prince Andrew refused to say in the BBC interview that he regretted being friends with Mr. Epstein, who killed himself in his Manhattan jail cell in August.