Dominic Cummings has been found in contempt of parliament after refusing to give evidence to an inquiry that found “foreign influence and voter manipulation” in the Brexit vote.

MPs have been urged to pass a formal motion condemning the head of the Vote Leave campaign for his “significant interference” in the work of the probe into “fake news”.

The call, from the Commons Committee of Privileges, follows Mr Cummings’ “total disregard” for parliament’s authority by rebuffing pressure to explain his role in the campaign, which broke the law.

Instead, the focus of Channel 4’s recent Brexit drama attacked the Digital, Culture, Media and Sport (DCMS) Committee for “grandstanding” and “spreading errors and lies”.

“The committee recommends that the house should admonish Mr Cummings for his contempt by way of a resolution of the house,” the Committee of Privileges concludes.

However, the episode has uncovered worrying weaknesses in parliament’s ability to force witnesses to attend hearings and to punish them if they refuse, the MPs say.

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MPs had previously decided its “penal jurisdiction” should be exercised as “sparingly as possible” – and stop short of any “power of committal to prison”.

“The Dominic Cummings case highlights the need for parliament to define in law what its powers should be to require witnesses to attend hearings and what sanctions should apply if they do not,” said Damian Collins, the DCMS Committee’s Conservative chairman.

“I’m calling for statutory powers to reassert the authority that is missing. The current powers have been tested to their limits and found wanting.”

Mr Cummings is widely seen as the brains behind the notorious “£350m-a-week for the NHS” claim emblazoned on bright red buses, despite it being proven to be false, and the “take back control” slogan.

As Vote Leave’s director, he made a show of refusing to work with Nigel Farage and Arron Banks – while admitting his campaign relied on their harsh anti-immigration messages.

Vote Leave has been referred to the police for busting campaign spending limits on the eve of the 2016 vote.

Crucially, the cash was used to pay data firm Aggregate IQ and – a whistleblower and an Oxford professor argue – potentially enabled it to precisely target enough voters on social media to have swayed the referendum result.

Theresa May has been criticised for downplaying the commission’s findings – even though they were to a “criminal standard of proof” – and has hailed the referendum as “a great exercise in democracy”.