A parliamentary report released in July said the government failed to find out whether Russia meddled in the 2016 referendum on membership of the EU, and recommended the intelligence services investigate further.
Johnson's government immediately rejected that recommendation and said it had not been complacent over the "enduring and significant threat" posed by Russia. Russia denied any interference.
The legal action launched on Thursday challenges Johnson's response and seeks a judicial review, claiming the government has breached the right to free elections enshrined in the European Convention on Human Rights.
"The sovereignty and security of our country, alongside the integrity of our democracy, is at stake, and this government’s wilfully turning a blind eye cannot be allowed to pass unchallenged," said Caroline Lucas, one of six lawmakers from parliament's upper and lower chambers named in the claim.
Leigh Day, the legal firm representing the group, said they were asking he court to step in to ensure that the government complied with its "legal duty to independently investigate credible allegations of Russian interference and to adequately protect future elections from foreign interference."
The university stands by the study but said the article was leading to the spread of 'misinformation'