Keir Starmer faces a vote on whether to launch an investigation into his decision to appoint Peter Mandelson as ambassador to Washington.

The speaker, Lindsay Hoyle, is expected to allow a debate on Tuesday on potentially referring the prime minister to the privileges committee over claims he misled the Commons, sources have told the Guardian. MPs are then expected to trigger a vote.

The vote is the latest test of Starmer’s authority, which has been damaged by the Guardian’s revelation that Mandelson was installed as ambassador despite the advice of vetting officials that he be denied security clearance.

Government whips are now considering whether to instruct Labour MPs to oppose any attempt to refer him to the committee.

The Tories have accused the prime minister of misleading MPs when he said “full due process” had been followed during the appointment process.

Knowingly misleading parliament is considered a resigning offence for ministers, and a privileges committee investigation in 2023 prompted Boris Johnson’s resignation as an MP. No 10 argues that Starmer was commenting on the facts he had available to him at the time.

However, opposition parties have pointed to a memo from Simon Case, the former cabinet secretary, who appeared to advise Starmer to complete security vetting for Mandelson before announcing an appointment. The Guardian, understands, however, that the document may have been intended to advise him simply to start the process.

The Conservatives have also accused Starmer of misleading MPs by suggesting that there was “no pressure whatsoever” applied on the Foreign Office, when Olly Robbins, the top official sacked over the affair, said last week there was.

Downing Street has said the prime minister’s comment about “pressure” referred to the security vetting process, rather than the broader appointment of Mandelson.

In an interview with the Guardian last week, David Lammy, the deputy prime minister, admitted there had been “some time pressures” on the Foreign Office last January to confirm Mandelson in post as Donald Trump was re-entering the White House.

“There was a feeling that obviously Trump had won the election in November, he was moving into the White House, and it would be good if we had an ambassador. So there were some time pressures around that I recall at the time.”

The government is likely to whip Labour MPs to vote against an investigation, making it unlikely the Conservatives will succeed. However, some Labour MPs may side with the opposition, giving a sense of the party’s discontent with the prime minister over the issue.