Sir Keir Starmer is facing a vote by MPs on whether there should be a parliamentary investigation over his claims about the vetting of Lord Mandelson.

Commons Speaker Sir Lindsay Hoyle said he was allowing a debate on the matter on Tuesday and it would then be up to MPs to decide if the Privileges Committee should hold an inquiry.

The prime minister has denied accusations he misled MPs over whether Lord Mandelson's vetting to be the UK's ambassador to the US followed "due process" and over his assertion that "no pressure whatsoever" was applied to officials at the Foreign Office.

No 10 branded the move "a desperate political stunt by the Conservative Party", which had asked for the vote.

Conservative leader Kemi Badenoch said Sir Keir had misled Parliament "multiple times" on the subject.

She urged Labour MPs to "look into their consciences" and back an inquiry by the Privileges Committee.

A Downing Street spokesperson said: "The government is engaging with the two parliamentary processes that are already running on Peter Mandelson's appointment with full transparency.

"This is a desperate political stunt by the Conservative Party the week before the May elections because they have no answers on the cost of living or the NHS. Their claims have no substance."

The government holds a majority in the House of Commons, so a large number of Labour MPs would have to vote for an inquiry or abstain in order for one to be launched.

The Privileges Committee can look into cases of MPs breaking parliamentary rules and in 2023 it ruled that the former Prime Minister Boris Johnson had misled MPs about parties in Downing Street during Covid.

The Ministerial Code states that ministers who knowingly mislead Parliament are expected to resign, while any inadvertent error should be corrected "at the earliest opportunity".

At the start of parliamentary business on Monday, Sir Lindsay said "numerous" MPs, including the Conservative leader, had asked him to allow a vote on holding an inquiry.

He emphasised that his role was "as a gatekeeper" to ensure such votes were held "sparingly" and that he was not taking a view on the rights and wrongs of the case.

Lord Mandelson was sacked seven months after starting the Washington DC job over his friendship with the convicted sex offender Jeffrey Epstein.

Sir Keir apologised for making the appointment but has continued to face questions over whether the vetting process was rushed.

Speaking on Monday, Conservative leader Kemi Badenoch said there was "still a lot of information that doesn't add up".

"What I'm seeing is a prime minister who is saying whatever he needs to to save his own skin," she added.

She said Sir Keir had misled Parliament when he told MPs that "full due process" had been followed in the appointment process.

She also questioned the prime minister's assertion that "no pressure existed whatsoever" on the civil service to approve Lord Mandelson as the UK's ambassador.

Sir Olly Robbins, who was the senior civil servant in the Foreign Office until he was sacked by the PM, told the Foreign Affairs Committee last week that there was "constant pressure".

He added that this did not affect his decision to give Lord Mandelson security clearance to take up the role.

In an apparent effort to clarify his comments in Parliament, Sir Keir told the Sunday Times there are "different types of pressure".

"There's pressure – 'Can we get this done quickly?' – which is not an unusual pressure. That is the everyday pressure of government," he said.

A vote will take place on the same day that senior former government figures are due to give evidence to the Foreign Affairs Committee, including the prime minister's former chief of staff Morgan McSweeney and former senior civil servant at the Foreign Office Sir Philip Barton.

Liberal Democrat Cabinet Office spokeswoman Lisa Smart MP said: "Labour MPs must put principle before party and vote to refer Keir Starmer to the Privileges Committee.

"After years of sleaze and scandal under the Conservatives, the public rightly expect better from this Labour government, not the same old instinct to cover things up."

Reform UK's economic spokesman Robert Jenrick said the prime minister had "misled Parliament" and had "behaved appallingly".

However, he added: "Parliament needs to actually talk about the priorities of the British people, and that is not primarily about the ins and outs of Peter Mandelson."

Zack Polanski, leader of the Green Party of England and Wales, said there were "lots of questions about the prime minister's conduct" and that he would support an inquiry.

He added: "I do want to caveat this by saying I think all of this is a huge distraction from the toxic combination of low wages and high bills, and actually what I want to see is the government focusing on that."

Speaking to the BBC Radio 4's Today programme, Dame Emily Thornberry said her committee was investigating the appointment and that she did not want the Privileges Committee to be "duplicating the work we're doing".

"It may be that at some stage in the future, some of the questions haven't been answered, and it is decided that they are of sufficient importance that the Privileges Committee should be involved," she said.

"But I don't really see why we're doing it at the moment, apart from, potentially people trying to score points in advance of the local elections."

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