The Metropolitan Police Commissioner was quizzed over what inquiries have taken place into the allegations from Virginia Giuffre against the Duke of York.
Ms Giuffre claims she was trafficked by Jeffrey Epstein, Andrew’s former friend, to have sex with the duke when she was 17 and a minor under US law.
She's now launched legal action against the duke - who has vehemently denied the allegations in the past and has not commented on the lawsuit.
What have police said about the case? ITV News Correspondent Geraint Vincent speaks outside Scotland Yard
Appearing on LBC Radio on Thursday morning, Dame Cressida revealed she has asked officers to again review allegations connected to late convicted sex offender Epstein, having so far decided not to open an investigation.
Asked what inquiries have taken place into the allegations from Ms Giuffre concerning the duke, she said: "I’m not going to talk about individuals, but what I can say is that I think what you’re referring to is associated with Jeffrey Epstein, who I will talk about since he is deceased.
"And the position there is that we have had more than one allegation that is connected with Mr Epstein and we have reviewed those, assessed those, and we have not opened an investigation."
She said the force looked at three things: "Is there evidence of a crime, is this the right jurisdiction for this to be dealt with, and is the person against whom the crime is alleged still alive?
"We have concluded that there is no investigation for us to open and we haven’t," she said.
The Met chief added it was the "right decision" after advice from the Crown Prosecution Service and two reviews.
Dame Cressida added: "I’m aware that currently there is a lot more commentary in the media and an apparent civil court case going on in America and we will, of course, again review our position… but at the moment there is no investigation."
Asked if the duke is "above the law", she replied: "No-one is above the law."
She said the Met is "open to working with authorities from overseas", adding: "As a result of what’s going on, I’ve asked my team to have another look at the material."
Dame Cressida’s comments come after Ms Giuffre’s lawyer David Boies warned against anyone ignoring the US courts and claimed the duke’s legal team had "stonewalled" appeals for information.
Ms Giuffre is suing the duke for allegedly sexually assaulting her when she was a teenager, and has said it was "past the time for him to be held to account".
Her lawyers filed the civil suit seeking unspecified damages at a federal court in New York, where the court documents claim she was "lent out for sexual purposes" by Epstein, including while she was still a minor under US law.
Andrew is named as the only defendant in the 15-page suit, brought under New York state’s Child Victims Act, although Epstein and his former girlfriend Ghislaine Maxwell are mentioned frequently throughout.
British socialite Maxwell has pleaded not guilty to sex trafficking charges in Manhattan federal court, where she faces trial in November, while Epstein took his own life in a US federal jail in August 2019, a month after he was arrested on the same charges.
If the duke and his legal team do not engage in the civil proceedings, they are expected to continue without their input – with the court making its judgment in due course.
Andrew does not face the prospect of an extradition hearing as this only applies to criminal charges and not civil cases.
In his 2019 Newsnight interview with the BBC’s Emily Maitlis, Andrew denied claims that he slept with Ms Giuffre on three separate occasions, saying: "I can absolutely categorically tell you it never happened. I have no recollection of ever meeting this lady, none whatsoever."
The duke also said he has no memory of a well-known photograph of him with his arm around Ms Giuffre’s waist at Maxwell’s housein London, and has questioned whether it was his own hand in the image.