Boris Johnson is facing new rules to force him correct misleading statements to parliament after the Commons Speaker backed demands for tougher action to promote honesty in politics.

Amid a fresh row over the prime minister’s “lies” to MPs, Lindsay Hoyle supported a proposal for the cross-party Commons Procedure Committee to look into “how perceived inaccuracies could be corrected” as quickly as possible.

Johnson faced new charges of misleading parliament on Wednesday as he wrongly claimed Keir Starmer had opposed the Brexit trade deal.

The Scottish National Party’s Ian Blackford also used prime minister’s questions to challenge Johnson’s denial that he had said he would rather “let the bodies pile high in their thousands” than order a new lockdown. “Are you a liar, prime minister?’ Blackford asked.

Hoyle, who said Blackford’s question was “unsavoury” but in order, has thrown his weight behind fresh moves to correct the record after a meeting with six opposition party leaders on Tuesday.

The party leaders had written to the Speaker about multiple occasions where Johnson had made inaccurate statements in the Commons, including on carbon emissions, economic growth, nurses’ bursaries, hospital car parking, NHS spending, the Covid-19 track and trace app, and poverty in the UK.

A viral video by filmmaker Peter Stefanovic, highlighting and correcting some of the statements, has been seen more than 13 million times.

Under usual parliamentary convention, ministers are required to correct the record at the despatch box as soon as possible if they have been found to have made misleading statements to the Commons.

But Johnson has failed to do so on a range of issues, including a false claim that Labour had voted against a 2.1% pay rise for nurses.

The PM’s former press secretary Allegra Stratton refused 20 times to correct the record or apologise at the time, relying on the Speaker allowing a clarification by shadow health secretary Jonathan Ashworth.

A spokeswoman for the Speaker’s Office said: “Mr Speaker welcomed the meeting and the proposal to ask the Procedure Committee to look into how perceived inaccuracies could be corrected.

“He hoped such a measure would improve transparency in House of Commons proceedings.”

The Procedure Committee said: “The committee will consider any request it receives to look at the matter of ministerial corrections in the new session of parliament.”

The Greens’ Carolline Lucas, who joined Lib Dem leader Sir Ed Davey and Blackford for the meeting, said rules for honesty at the despatch box are designed for a less “Trumpian” era.

“He is a serial liar. This is a man who isn’t just lying occasionally, he is routinely lying at the despatch box and that makes it impossible for MPs to hold him to account,” she told BBC Radio 4’s Today programme.

Johnson sparked anger among Labour MPs when he said of Starmer in PMQs: “Last night our friends in the European Union voted to approve our Brexit deal – which he opposed.”

Shadow cabinet office minister Rachel Reeves said Johnson had “lied” because her party did not vote against the Brexit trade deal bill late last year – and in fact voted for it.

A spokesperson for Starmer told HuffPost UK: “This is yet another example of Boris Johnson misleading parliament. Labour voted for the government’s Brexit deal and the Prime Minister should come back to Parliament to correct the record.”

A No.10 spokesperson said: “It’s a matter of public record that they did vote in favour of that, but the broader point is Keir Starmer has consistently backed a second referendum and said he would vote to remain.”

She denied that the PM had been “sloppy” with his language, adding “I think he was very clear in the comments.”