Police have held discussions with specialist prosecutors over investigations into Andrew Mountbatten-Windsor’s links with Jeffrey Epstein while the former duke was acting as the UK’s trade envoy.

Oliver Wright, assistant chief constable of Thames Valley police, said on Wednesday that the force was leading the assessment of allegations against Mountbatten-Windsor of misconduct in public office, specifically relating to documents within the Epstein files released by the US justice department.

“As part of this assessment, we have engaged in discussions with specialist crown prosecutors from the CPS [Crown Prosecution Service],” Wright said.

He added: “We will provide updates as and when they are available, but at this stage it would be inappropriate to discuss further specifics of this work.”

Wright said information was evaluated during an assessment phase to determine whether a criminal offence was suspected and a full investigation required.

“Allegations of misconduct in public office involve particular complexities, and therefore an assessment must be conducted carefully and thoroughly,” he said. “While we cannot provide timescales over when a decision as to whether a criminal investigation will be opened, we can assure you that Thames Valley police is making progress as quickly as possible.”

Thames Valley police previously said it was reviewing allegations that the child sex offender Epstein provided Mountbatten-Windsor with a woman to have sex with at Royal Lodge in 2010, as well as that the former prince shared confidential reports from his role as a government trade envoy with the disgraced financier.

The Met police has also launched an investigation into allegations Peter Mandelson leaked Downing Street emails and market-sensitive information to Epstein.

At a press briefing earlier on Wednesday, the director of public prosecutions for England and Wales, Stephen Parkinson, said the CPS was in “close contact” with the Met and Thames Valley police, but it had not been asked for formal advice yet.

“In complex and sensitive cases, the CPS and the police do work together. And I’m sure, in respect of the investigation that has been announced, we will do so.”

However, he said at the time that the CPS would not be giving “step-by-step updates”.

The allegations stem from documents released by the US Department of Justice relating to Epstein and his links to the rich and powerful.

Emails released appeared to show Mountbatten-Windsor sharing reports of official visits to Hong Kong, Vietnam and Singapore. Buckingham Palace responded by saying that it was “ready to support” any police investigation into Mountbatten-Windsor.

The Met is investigating Mandelson for alleged misconduct in public office in relation to emails containing market-sensitive information that he apparently sent to Epstein while the former Labour peer was business secretary during the financial crisis.

The emails showed Mandelson claiming he was “trying hard” to change policy on bankers’ bonuses, sharing details of an imminent bailout package for the euro the day before it was announced, and suggesting that the JP Morgan boss “mildly threaten” the chancellor.

Parkinson said he was confident that the CPS could advise the police over the offence of misconduct in public office, despite widespread concerns that the common law offence, which is in the process of being replaced by a statutory offence, is ill-defined and lacks clarity.

He said: “The issue when you’re advising on criminal cases, it’s very rarely about what the law is, it’s about the application of the law in the context. I’m confident we would be able to give advice.”

The revelations prompted fresh scrutiny of Keir Starmer’s decision last year to appoint Mandelson as US ambassador. Starmer’s chief of staff, Morgan McSweeney, quit on Sunday, saying he took “full responsibility” for advising Starmer on the appointment, but his departure has failed to relieve the pressure on the prime minister.

Mandelson has said that none of the recently released Epstein files “indicate wrongdoing or misdemeanour on my part”.

Mountbatten-Windsor, who served as the UK’s special representative for trade and investment between 2001 and 2011, has always denied any wrongdoing.