Theresa May knew leave campaigners may have breached financial limits during the EU referendum campaign when she triggered article 50 initiating Brexit, her lawyers have admitted.

In a formal response to a high court challenge over the legitimacy of the vote, lawyers for the prime minister have been attempting to dismiss the action brought by Britons living in France, Italy and Spain.

By suggesting flaws in the referendum process were already anticipated, Joseph Barrett, the barrister who wrote the response, has implied there was nothing new for the court to investigate.

The rival submissions and responses were released on Monday by lawyers acting for the organisation UK in EU, which had crowdfunded the legal challenge.

Its claim argued that the Electoral Commission’s findings on BeLeave and Vote Leave, which resulted in two officials being reported to the police and fines being imposed, mean the 2016 EU referendum was not a lawful, fair or free vote.

Barrett, a barrister at 11KBW chambers in London, argued: “The allegation of ‘error of fact’ upon which the claim is predicated is unsustainable … At the time the decision to give article 50 notice was taken, it was a matter of public record that campaigners may have breached campaign finance requirements, and other requirements, during the EU referendum campaign.

“The contention that the decision to give article 50 notice was founded on a premise that there had been universal compliance with those requirements is therefore incorrect and unarguable.”

He added: “Allegations that there had been breaches of campaign finance limits etc during the EU referendum campaign were a matter of public record at the date of giving article 50 notification, and it was also a matter of public record that such allegations were being investigated by the Electoral Commission (and might be found to be made out).”

Barrett also argued that the claim was out of time, that the prime minister’s decision was reasonable at the time she made it in March 2017, and that if the claimants win there would be “the clearest possible detriment to good administration”.

On Monday evening, Tory and Labour MPs rejected calls to withdraw article 50 over Vote Leave’s overspending, despite almost 200,000 people signing a petition calling for it to be rescinded.

In a debate in Westminster Hall, triggered by the petition, the Brexit minister Chris Heaton-Harris said that while the government “respects the views and wishes” of those who signed the petition, the referendum result was one that “cannot be ignored”.

And the shadow Brexit minister Paul Blomfield said the law did not provide for overturning referendum results for cheating.

Sue Wilson, the lead claimant and chair of Bremain in Spain, commenting on the government’s response to the high court challenge, said: “We took the decision to publish the summary grounds of resistance and our response in order to provide complete transparency about the challenge and the repercussions of the Vote Leave campaign for members of the public.

“We must be able to trust in the democratic process and to be sure that votes and power can’t be bought. If the prime minister was aware of the allegations of cheating during the referendum at the time she sent her letter giving notice for the UK to withdraw from the EU – as appears to be the case here – she needs to be held accountable.”

Rupert Croft, the managing director of Croft Solicitors, which has been acting for the claimants, said: “The next step is for a high court judge to decide how the case should proceed. We have requested that a hearing is listed on an expedited basis to decide the claim. We believe that the claim is of significant constitutional importance, but unless it’s heard quickly there’s a risk it will become academic.”

Charlie Mullins, the founder of Pimlico Plumbers, who funded the first court challenge against article 50, said: “The Vote Leave campaign, the official group fronted by Boris Johnson and Michael Gove, has been found guilty of breaking electoral law during the 2016 referendum campaign, and the government is actively blocking legal claims that this crime means Theresa May illegally triggered the UK’s withdrawal from the EU.