The government must urgently legislate to ensure digital campaigning is covered by electoral law, rather than hoping Britain will not have a general election until 2022, a parliamentary committee has warned.

Under current law, Britain is not due to have a “major” election until the Scottish parliamentary vote in May 2021. But the digital, culture, media and sport (DCMS) committee has warned that planning on such a basis is shortsighted.

“The government cannot work on the basis of elections not taking place before 2021. Were an election or referendum to take place later this year, campaigns would be fought using electoral law that is wholly inadequate for the digital age. As a result, we believe that urgent legislation should be brought forward at once to bring electoral law in line with digital campaigning techniques.”

The committee made the criticism in a report responding to the government’s online harms white paper, which was published in April. In their response, MPs criticised the government for ignoring their advice “particularly that a category should be introduced for digital spending on campaigns; and that information about all political advertising material should be searchable in a public repository.

“There was no acknowledgement” in the report, the MPs added, “of the risks of foreign investment in elections, for example via digital payments, or of the role and power of unpaid campaigns and Facebook groups that influence elections and referendums (both inside and outside the designated period). The steps taken voluntarily, for example, by Facebook to identify political advertising and those associated with it have been very limited and do not adequately meet public concerns.”

In June, the electoral commission warned the Brexit party was at high risk of accidentally accepting illegal foreign donations, due to a PayPal link on the party’s website. The party was told to check all donations came from legitimate sources by the commission, whose director of regulation, Louise Edwards, said: “They need to go back and look at the payments they have received, over or under £500, and they need to satisfy themselves that they are sure those amounts of money are permissible. And if they are not, they need to forfeit those amounts of money.”

In the white paper the government proposed a raft of regulations for the internet, built primarily around the creation of a regulator and the introduction of a “duty of care” requirement for social media firms and other companies that traffic in user-generated content online.

But the focus of the white paper was largely on harms to the individual, such as harassment, hate speech and material promoting suicide and self-harm. Other than the suggestion of a requirement for platforms to deal with online misinformation, it spent little time addressing the harms to society and democracy that can come from an unregulated internet.

The information commissioner, Elizabeth Denham, singled out the absence of any new regulation on political advertising as one such oversight. “It is surprising and concerning to me that the government have not done a comprehensive examination of political advertising and the oversight that is needed in this space,” Denham told the committee. “It is a gap that really needs to be addressed.”

Damian Collins, the chair of the DCMS committee, said the government needed to rectify that error by introducing urgent legislation above and beyond the online harms white paper. “We know that our electoral laws are not fit for purpose. Political campaigns are fought online, not through the letterbox, and our laws need to be brought up to date with the digital age. We’ve repeatedly highlighted threats to our electoral system and it’s essential that public confidence is restored.”

Other than the lack of regulation around electoral interference, MPs had one other piece of advice: that they be given veto power over the appointment of the chief executive of the new regulator. “Select committees can act as important guarantors of independence and confidence in the public appointments process,” the committee argued, citing the fact that the Treasury committee has veto powers over the leadership of the Office for Budget Responsibility.