A cross-party group of MPs is demanding new powers that would force witnesses to give evidence before parliament or face possible imprisonment, as anger grows over the refusal of the former Vote Leave director, Dominic Cummings, to answer claims that the organisation that helped to deliver Brexit broke electoral law.

Pressure for parliament to be able to force attendance is coming from senior parliamentarians, including the chairs of several powerful select committees. A parliamentary report from the all-party digital, culture, media and sport (DCMS) committee is also expected to call for parliament to have the ability to demand attendance, backed by the threat of sanctions, this week.

Anger at Cummings’s refusal to come before MPs has intensified since Vote Leave was fined £61,000 and referred to the police after the Electoral Commission found last week that it had broken electoral law. The watchdog ruled it had exceeded its £7m spending limit by funnelling £675,315 through the pro-Brexit youth group BeLeave – details of which were revealed in the Observer.

The founder of BeLeave, Darren Grimes, was fined £20,000 and referred to the police, along with Vote Leave official David Halsall. Cummings, who escaped censure, had previously been asked by the DCMS committee to give evidence over claims of rule-breaking but refused, accusing MPs and the Electoral Commission of “grandstanding”.

The Observer understands that an interim report by the DCMS committee, chaired by Tory MP Damian Collins, will call within days for an inquiry into how to beef up the powers of parliament to ensure people called to give evidence cannot simply refuse to attend.

Last night a Labour member of the DCMS committee, Paul Farrelly, said: “There is no point in us huffing and puffing about this and allowing people like Cummings to thumb their noses at us. Parliament was the institution that Cummings wanted power to be restored to. The Electoral Commission has now found that Vote Leave broke electoral law. We will certainly call for an urgent examination of how to give the House powers to summon witnesses in the digital age. This should be carried out by the House of Commons Standards committee.”

In an interview with the Observer, Vote Leave volunteer Shahmir Sanni, who blew the whistle on co-operation between Vote Leave and BeLeave this year, said neither the politicians behind the Vote Leave campaign – Michael Gove and Boris Johnson – nor the officials at the top of the organisation were being held to account.

“This debate is no longer about Brexit. It is simply about the law and how democracy was perverted by the breaking of it. None of the directors of Vote Leave or the ministers on its board and committees have been held to account. There are people who oversaw this illegal activity still working in government, deciding the future of this country.

“The sheer disrespect that Dominic Cummings has shown toward parliament and that [former Vote Leave chief executive] Matthew Elliott has demonstrated in interviews toward our authorities is testimony to how tainted Westminster has become. Everyone involved must be held to account, otherwise we’re going to lose a lot more than just cheap flights to Europe come March 2019.”

An Opinium poll shows that 66% of the public believe Vote Leave’s behaviour in breaking electoral law is a “serious matter” – as opposed to 17% who do not. Some 40% think the behaviour affected the result of the referendum while 41% do not.

Several other heads of select committees spoke out to demand that parliament have power to summon witnesses, and a new system with sanctions including fines or imprisonment if they refuse to do so.

Sarah Wollaston, who chairs both the health and social care select committee and the liaison committee, which comprises all chairs of select committees, said: “It is the height of hypocrisy that someone who ran a campaign that emphasised returning powers to parliament now refuses to appear before MPs. Now that there is a judgment [from the Electoral Commission] against Vote Leave it is even more important that he appears to explain what was going on.”

Nicky Morgan, chair of the Treasury select committee, said: “The select committees are a vital part of democracy. Refusing to appear in front of one isn’t just about snubbing parliament: it’s about deliberately turning your back on our democracy. Someone who asked voters for their trust just two years ago should behave better.”

The former Attorney General Dominic Grieve, who chairs the intelligence and security committee said: “It is time for parliament to devise a new system that enables people to be summoned, backed by proper sanctions should they refuse to do so.”

The Labour MP Hilary Benn, who chairs the Brexit select committee said: “Vote Leave may have won the referendum but they are now rightly being held to account both for the promises they made and for their behaviour in fighting it. The more this scrutiny reveals, the less some of the individuals involved appear to want to be associated with their role and its consequences for the country. Day by day, however, we are learning how wrong they were.”

Cummings was not available for comment on Saturday. Vote Leave responded to last week’s Electoral Commission report by saying it was “wholly inaccurate” and “politically motivated”.

More than 40 MPs called on Friday for far-reaching changes to the UK’s electoral system, which was described as unfit for purpose and in dire need of reform. Stephen Kinnock, whose letter to the speaker, John Bercow, was signed by 45 Labour, Lib Dem and Green MPs, said the existing fines were an insufficient deterrent and were regarded as “simply as the cost of doing business”.