Scotland Yard is reviewing allegations that Peter Mandelson leaked confidential Downing Street emails and market-sensitive government information to the disgraced financier Jeffrey Epstein.
Documents released by the US Department of Justice suggest Mandelson shared privileged information on at least four occasions while serving as business secretary in 2009.
The SNP and Reform UK have reported Peter Mandelson to the Metropolitan Police.
The Leader of the SNP in Westminster - Stephen Flynn - said in a letter to the Met Police commissioner: "If such allegations are investigated and proven, it is gravely serious – for Peter Mandelson, for the Labour Prime Ministers who appointed him and for the UK Government as a whole.
"That is why I believe it is now clearly in the public interest that all of these newly released emails and files, and Mandelson’s entire period in UK Labour Governments, must now be criminally investigated."
The Metropolitan Police said it would review whether the disclosures meet the threshold for a full investigation into misconduct in public office.
Downing Street said the prime minister was “very clear that he should not be a member of the House of Lords or use the title”, but added that removing Mandelson’s peerage through legislation would be “complex”.
Former prime minister Gordon Brown described the information in the Epstein files as “shocking” and called for an investigation.
Mandelson has resigned from the Labour Party following the release of the documents.
In an interview with The Times, he said: “The decision wasn’t easy but I feel better for it as I need to reset… I want to be an outsider looking in and not the other way round.”