ReutersAndrew Mountbatten-Windsor's time as trade envoy should be investigated for possible corruption, a former business secretary said.
Files released by the US department of Justice appear to show the former prince forwarded UK government documents and other commercial information to the convicted sex offender Jeffrey Epstein.
Speaking about reports of Andrew leaking sensitive information about the Royal Bank of Scotland (RBS) and Aston Martin while trade envoy, Sir Vince Cable, said his behaviour was "totally unacceptable".
Andrew has always consistently and strenuously denied any wrongdoing.
Sir Vince, who was secretary of state for business and trade for some of the former duke's time as trade envoy, said: "We need a police or DPP [director of public prosecutions] check on whether criminal corruption took place and a government investigation into how this was allowed to happen".
In his role as a UK trade envoy - which ran from 2001 to 2011 - the then-Duke of York travelled globally and enjoyed privileged access to senior government and business contacts around the world.
In 2010, he apparently passed on an email conversation about Aston Martin and the Royal Bank of Scotland to a contact, David Stern, who passed it on to disgraced financier Epstein.
That conversation with Terence Allen, an investment banker based in Abu Dhabi, has some details of RBS's plans to restructure, and unflattering reflections on the chief executive, Stephen Hester.
The email also describes "conflicts between internal parties" at Aston Martin.
The BBC has contacted Stern for comment.
It is not clear how much of this information came from his role as trade envoy. Andrew was a customer of RBS, and may have spoken to the management in that capacity, or in another.
The bank was majority owned by the taxpayer at the time.
The same year, Andrew appears to have forwarded government reports from visits to Vietnam, Singapore and China to Epstein, according to the recently published files.
Emails from a different source have also emerged suggesting he passed on information about Iceland from the Treasury to a banker contact of his, Jonathan Rowland.
According to official guidance, trade envoys have a duty of confidentiality over sensitive, commercial, or political information about their official visits.
Thames Valley Police on Wednesday said it had spoke with specialists from the Crown Prosecution Service about allegations that Mountbatten-Windsor shared confidential reports from his role as the UK's trade envoy with Epstein.
Labour MP and women and equalities committee chair Sarah Owens said Mountbatten-Windsor must face questions from police and Parliament, while her colleague Rachael Maskell told the BBC Mountbatten-Windsor had been "conservative with the truth".
"We need to know what was happening in those circles and therefore I think it would be right to be able to scrutinise, have transparency and to get to the bottom of all these dealings," Maskell said.
Maskell said Andrew should also be stripped of his succession rights to the throne, as well as a councillor of state.
"All of these titles and positions need to be addressed so we're just left with Andrew the citizen and a citizen that is fully accountable," she said.
The King has spoken of his "profound concern" over the allegations of misconduct against his brother, and Buckingham Palace said it stands "ready to support" the police if approached.
The former prince continues to be dogged by his links to Epstein after the latest tranche of documents released by the US government included pictures of Mountbatten-Windsor, fully clothed, kneeling on all fours over a woman lying on the ground.
He is facing growing pressure to testify in the US about his links to Epstein and last week moved from his Windsor home to the Sandringham Estate in Norfolk.
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