The chief strategist of the Vote Leave campaign has refused to appear in front of MPs, risking possible censure from the House of Commons but also raising questions about what more can be done when a witness ignores the will of parliament.

Dominic Cummings, who has been credited as the brains behind the successful Brexit campaign, told the select committee investigating fake news that he would not be willing to answer questions in public before the Electoral Commission finishes its ongoing investigation into his campaign.

The digital, culture, media and sport committee said this was not a valid excuse and issued a formal summons through parliament’s serjeant-at-arms, demanding that Cummings appear before it by the end of May.

Cummings rejected this summons, angering MPs on the committee who wanted to ask questions about the use of Facebook data during the EU referendum campaign.

The committee confirmed that Alexander Nix, the former boss of Cambridge Analytica, had accepted a formal summons to appear on 6 June.

“We are disappointed that Dominic Cummings has not responded positively to our requests for him to appear,” said the committee’s chair, Damian Collins. “Reporting the matter to the house is a first step, which could result in a decision that a contempt of parliament has been committed, a very serious outcome for the individual.”

However, the refusal raises questions about the system of compelling reluctant witnesses to appear in front of parliament. It is the second time this week that a potential witness has turned down a formal summons to answer questions from MPs, after Facebook’s Mark Zuckerberg turned down a request from the same committee.

In theory, parliament has the power to issue fines or even threaten imprisonment for non-attendance. In reality, the system relies largely on consent, formal rebukes and the idea that individuals can be shamed by the media into attending.

Hannah White, of the Institute for Government, a thinktank, has previously said there are serious risks in issuing such summons if they are ignored. “Every time everyone observers the emperor has no clothes, in that parliament can’t force people to come, they lose a little bit of their authority.”

Cummings, who will be played by Benedict Cumberbatch in a forthcoming TV drama about Brexit, published a blog this week in which he explained his decision, saying lawyers had told him to “keep my trap shut” until the Electoral Commission completes its investigation into Vote Leave this summer.

He said he had been willing to give evidence to the committee after this date, but the MPs’ decision to issue a formal summons via the media showed their priority was “grandstanding PR, not truth-seeking”.

Cummings said he believed select committees should have the legal power to compel witnesses to attend. However, since no such law was in place, he said, he would not now give evidence “under any circumstances”.

The committee system needed reforming to include “processes that push them towards truth-seeking behaviour rather than the usual trivialising grandstanding,” he said. “So far the inquiry on fake news has helped spread fake news across the world.”