Campaigners are preparing to launch a legal challenge against the government’s refusal to hold a Mueller-style inquiry into potential interference in the Brexit referendum.

Solicitors acting on behalf of the Fair Vote UK pressure group have sent a pre-action letter to ministers over Theresa May’s decision not to pursue an independent probe into “irregular and unlawful conduct” that sought to influence the result of the 2016 vote.

Their concerns centre on the extent of Russian disinformation, the involvement of foreign data firms such as Aggregate IQ, and breaches of electoral spending rules by Vote Leave, the official Brexit campaign.

The prime minister rejected calls for a public inquiry into the integrity of the referendum process last month, arguing it was a thinly-veiled attempt to overturn the result of the Brexit vote.

However, senior MPs, including Damian Collins – the Tory chairman of the Digital, Culture, Media and Sports Committee – and shadow culture secretary Tom Watson, have said the UK needed a probe similar to special counsel Robert Mueller’s investigation into Russian interference in the 2016 US elections.

Mr Watson said: “Mueller has shown that we need to follow the money – and the lies – to get to the truth about how votes are unfairly won.

“Given what we know about law-breaking, Russian involvement and massive data abuse issues, it is essential that we have a full public inquiry into what happened in the referendum.

“We need to know what went wrong so we can fix it and safeguard our democracy.”

A recent report into fake news by the DCMS committee said MPs had heard evidence of “Russian state-sponsored attempts to influence elections in the US and the UK through social media, efforts of private companies to do the same, and law-breaking by certain Leave campaign groups in the UK’s EU referendum in their use of social media”.

Mr Collins, who has clashed repeatedly with Vote Leave bosses and tech giants, warned of “a crisis in our democracy – based on the systematic manipulation of data to support the relentless targeting of citizens, without their consent, by campaigns of disinformation and messages of hate”.

He has since called for a police inquiry, telling The Times: “We have been operating at the limits of our powers in this inquiry. We’ve done things that no select committee has ever done before, but we do not have the powers that a law enforcement agency has.

“We do not have the power that Mueller has to demand to see bank records, private papers and other things.”

Lawyers acting for Fair Vote UK said there was a “compelling case” for an inquiry to carry out investigations into wrongdoing, and their arguments are in the hands of the electoral watchdog, MPs and the Information Commissioner’s Office (ICO).

The Electoral Commission fined and referred Vote Leave to the police over breaches to electoral spending rules this year, something the Brexit campaign group has denied was politically motivated.

John Halford, of Bindmans LLP, said: “The basic problem with unethical and undemocratic conduct of the kind that occurred throughout the referendum campaign is that it rarely occurs openly.

“It lurks in the gaps between outdated laws, and advances through covert collaboration and with the help of foreign states and companies. As the US experience shows, special powers are needed to bring it into the light.”

Kyle Taylor, Director of Fair Vote UK, said the organisation was challenging the national vote due to ”significant public concern” about the referendum process.

Brexit: 10 of the most ridiculous headlines Show all 10 1 /10 Brexit: 10 of the most ridiculous headlines Brexit: 10 of the most ridiculous headlines The Sun, March 9 2016 This wholly false headline merited the first ruling by IPSO (the press regulator) under clause 1 of the revised Editor's Code of Practice. Clause 1 makes specific reference to newspapers printing "headlines not supported by the text" Brexit: 10 of the most ridiculous headlines Daily Mail, November 4 2016 In perhaps the most notorious front page of the past few years, the Mail derides the High Court judges who ruled that parliament must have a vote on whether to trigger article 50 and start the Brexit process Brexit: 10 of the most ridiculous headlines Daily Express, November 4 2016 In the Express' take on the same story, they manage to incorporate the Union Jack, allude to First World War propaganda, invoke memories of Churchill and, of course, state "Brexit means Brexit" Brexit: 10 of the most ridiculous headlines The Sun, March 29 2017 The Sun marked the day on which Mrs May triggered article 50 by projecting a huge and terrible pun on to the Cliffs of Dover Brexit: 10 of the most ridiculous headlines The Sun, April 4 2017 Referencing their notorious eurosceptic headline from 1990 (See: Up Yours Delors), the Sun stokes the flames of the brief Gibraltar dispute, a dispute in which Spain, the supposed aggressors, only joined to note that there was "no need for it" Brexit: 10 of the most ridiculous headlines Daily Mail, April 19 2017 This headline followed Mrs May's snap election announcement, which gave the Mail hope that dissenting opinions on Brexit would disappear Brexit: 10 of the most ridiculous headlines Daily Mail, December 14 2017 In recent months, the Mail has often forgone catchy headlines in favour of rambling rants, this is an early example aimed at Tory Brexit rebels Brexit: 10 of the most ridiculous headlines Daily Mail, January 31 2018 This headline (?) takes aim at the Lords over their repeated amendments to the EU Withdrawal Bill Brexit: 10 of the most ridiculous headlines The Sun, June 12 2018 On the day that the EU Withdrawal Bill is to be debated in the Commons, the Sun offers two choices to MPs, desperately including all conceivable imagery that might make Brits feel patriotic, which apparently includes the Loch Ness Monster Brexit: 10 of the most ridiculous headlines Daily Express, June 12 2018 On the same day, the Express lets MPs know what the consequences of the vote may be

The campaign has raised more than £25,000 to crowdfund the judicial review, but still needs to generate £75,000 to fund the full costs of the legal challenge.

The legal challenge could face stiff opposition from the government, as Ms May’s lawyers argued the calls appeared to be “a collateral, and poorly concealed, attack on the giving of Article 50 notification and/or the referendum outcome”.

According to the legal letter, government lawyers said: “The objective appears to be to undermine/disrupt the government’s ongoing treaty negotiation with the EU27. In the circumstances, this claim is also non-justiciable.”