"I'm afraid to say that I don't believe that photograph was taken in the way that has been suggested".
During his Newsnight interview, Prince Andrew said he could not recall ever meeting Ms Giuffre and said that on the night she claims they first met that he went to Pizza Express in Woking and then returned home.
"In August 2019, following the death of Jeffrey Epstein, the MPS reviewed the decision making and our position remains unchanged", the police said.
It comes after the UK's Metropolitan Police Service said today it would not reopen an investigation into an "allegation of non-recent trafficking for sexual exploitation" it received from Ms Giuffre in 2015.
A television interview with Giuffre is scheduled to be broadcast Monday (Sunday NZ time) in Britain. The allegation was made against a USA national, Jeffrey Epstein, and a British woman.
"The MPS has liaised with other law enforcement organisations but has not received a formal request asking for assistance in connection with this allegation", it added. "It related to events outside of the United Kingdom and an allegation of trafficking to central London in March 2001", United Kingdom police said in a statement.
But police said in a statement the investigation was dropped because it primarily involved figures outside of the UK.
"He [Prince Andrew] knows what happened, I know what happened, and there's only one of us telling the truth".
Metropolitan Police Commander Alex Murray said police concluded in 2016, after looking into the matter and consulting prosecutors, that it was the wrong agency to investigate.
Prince Andrew has suggested this image of him with Giuffre is fake.
There have also been reports that Buckingham Palace are braced for the arrival of a subpoena summoning Andrew to testify in the ongoing Epstein investigation in the United States, with sources claiming it's only a matter of time before he is called upon.
The third time, when she was just 18 years old, allegedly took place when she and the Duke of York were "in an orgy on Epstein's private island in the U.S. Virgin Islands".
The interview has been widely considered a public relations disaster for Andrew, who announced shortly after it aired that he would be stepping down from his royal duties.