Lord Doyle, a veteran Labour spin doctor who was the party’s head of press between 1998 and 2005 before working for Lord Blunkett and Sir Tony Blair, was given a peerage by Sir Keir in December. He was sworn in as a member of the House of Lords last month.

The Sunday Times first reported about Lord Doyle’s campaigning for Morton in December last year and last week the Conservatives called for details of the peer’s vetting to be published.

A Labour Party spokesperson said: “All complaints are assessed thoroughly in line with our rules and procedures.”

The party is undertaking an investigation and Lord Doyle’s Labour whip in the House of Lords has been withdrawn while this is ongoing.

Sir Keir faced questions about Lord Doyle’s peerage on Monday during a meeting of the Parliamentary Labour Party, when the prime minister rallied MPs behind his leadership.

Conservative leader Kemi Badenoch wrote to Sir Keir last week to call on him to “explain why you appointed another friend of a child sex offender to a prestigious post”.

It comes after the PM confirmed he had appointed Lord Mandelson to the role of US ambassador despite knowing about his friendship with convicted sex offender Jeffrey Epstein.

The PM apologised to Epstein’s victims for believing Mandelson’s “lies” about the extent of his relationship with the financier.

After Lord Doyle was suspended, Badenoch said the PM must “come clean about what he was told” before making Doyle a peer, adding: “We won’t let this go.”