Whether a prime minister misled parliament is a serious matter. The pattern of statements made by Sir Keir Starmer about appointing Lord Mandelson as US ambassador may justify a parliamentary sleaze inquiry. Opposition parties claim that the prime minister misled MPs over the process that led to the peer taking the Washington job. But they would say that, wouldn’t they? More troubling is that in Tuesday’s Commons debate some Labour MPs either abstained or defied the whip and voted to refer the matter to parliament’s privileges committee ahead of next week’s elections. Such rebellion speaks to disillusionment with Sir Keir’s leadership.

The prime minister has confessed to making a “mistake” in appointing Lord Mandelson despite knowing that he maintained a friendship with Jeffrey Epstein after the financier’s conviction for child sexual abuse offences. But it was Morgan McSweeney, who backed Lord Mandelson for the job, and Sir Olly Robbins, the head of the Foreign Office, who did not draw vetting concerns to Sir Keir’s attention, who both lost their jobs. Voters plainly think it wrong that others have paid for Sir Keir’s blunder.

The issue on Tuesday was not that the prime minister said something untrue in the House. It is that he seemingly presented a partial account that made it difficult for MPs to understand the decision they were being asked to scrutinise. Sir Keir told the Commons last week that “no pressure existed whatsoever”. Such a categorical statement did not survive contact with reality. On Tuesday Mr McSweeney admitted pressuring the Foreign Office to expedite Lord Mandelson’s role.

The prime minister told MPs that “full due process was followed”. But that rests on a narrow definition of process as the completion of formal steps. Evidence suggests that Downing Street ignored advice from the then cabinet secretary to get security clearance before announcing Lord Mandelson’s appointment. Both Sir Philip Barton, who was in charge of the Foreign Office at the time of the peer’s appointment, and the department’s head of security, Ian Collard, testified that the Cabinet Office initially suggested Mandelson was exempt because he was a privy counsellor and a member of the House of Lords. The Cabinet Office disputes this claim.

Sir Philip’s evidence is particularly problematic. He admitted deep reservations about Lord Mandelson’s ties to Epstein, fearing a “toxic hot potato”, but said he had “no space” to raise them after being presented with a fait accompli by No 10 – and left his job before vetting took place. There may be worse to come.

The prime minister said the UK Security Vetting agency recommended clearance “should be denied”, and expressed outrage that he was kept in the dark about this rejection. Yet while UKSV warned in its 10-page summary of high concern and advised refusal, Mr Collard claims its “final … assessment” was that the case was “borderline” and envisaged security clearance with “robust risk management”. What Sir Keir judged as clearcut, the Foreign Office’s director of security says was anything but.

The bad news for Sir Keir is that voters back an inquiry into whether he misled MPs over the Mandelson case by three to one. The prime minister’s survival may hinge on the May elections. The Mandelson saga reflects not just questions of Whitehall process but of a prime ministerial lack of curiosity and judgment. With more documents to come and the foreign affairs committee investigating, the facts are still emerging – and they may get worse.