In a motion backed by MPs last week, the government agreed to publish all documents relating to Lord Mandelson’s appointment as the UK’s ambassador to the US.

The government agreed that sensitive documents would be referred to Parliament’s Intelligence and Security Committee of Parliament (ISC), a group of MPs which will have a role in deciding what will be published.

One source said following Streeting’s move to publish messages himself, there was now concern that ministers could feel political pressure to publish messages that should instead be shared by the ISC.

When Environment Secretary Emma Reynolds was asked if she would follow Streeting’s example, she told BBC Newsnight: “Yeah sure, I have nothing to hide.”

In a statement on Tuesday, a Met Police spokesperson said the force would “review material identified and provided to us by the Cabinet Office to assess whether publication is likely to have a detrimental impact on our investigation or any subsequent prosecution”.

The spokesperson added: “We will work alongside the Cabinet Office to review relevant documents over the weeks ahead.

“The process to decide which documents should ultimately be published remains a matter for government and parliament.

“As we have stated previously, this investigation may be complex but we are focused on a timely and thorough process so that justice is served in this case or future ones linked to the Epstein files.

“We understand and respect the role of Parliament in releasing these documents and will support their objective of transparency through our work with the Cabinet Office.”

The government has started gathering the files, which could total 100,000 and include potentially embarrassing private messages between Lord Mandelson and ministers, officials and special advisers.

But the government has not indicated when it plans to publish any of the material – or whether it will be released in batches or all in one go.

The prime minister sacked Lord Mandelson last year when new information about his relationship with Epstein came to light.

Sir Keir has claimed the vetting documents will show Lord Mandelson lied to him about the extent of his friendship with Epstein, which continued after the disgraced financier had been convicted in 2008.

The BBC understands Lord Mandelson’s view is that he answered questions about his relationship with Epstein in the vetting process accurately.