The Crown Prosecution Service (CPS) is considering investigating a complaint arguing voters were misled by the Vote Leave and Leave.EU campaigns in breach of electoral law.
The complaint was submitted by an independent group led by Professor Bob Watt, an expert in electoral law at the University of Buckingham, The Guardian reports.
Mr Watt said the complaint about "undue influence" on the referendum campaign centres on allegations the leave campaigns made "assertions of fact that were knowingly misleading" - including the high-profile claim the EU was costing the UK £350 million a week.
He said the Vote Leave claim was contrary to evidence from the Office of National Statistics. Nearly half of Britons believed the claim in the run up to the EU referendum, an Ipsos MORI poll found.
The professor also cited as misleading Vote Leave's claim "the UK has no border controls whilst in the EU" and posters claiming "Turkey is joining the EU".
Normally, the police have to lodge a complaint before the CPS can consider it, but under the Representation of the People Act 1983, the director of public prosecutions can consider alleged election offences which are referred directly to the CPS.
"Undue influence" is considered a corrupt practice under electoral law.
Although the case would have no influence on the EU referendum result if brought successfully, it could result in criminal charges for anyone the courts hold responsibile for making false statements.
Leave.EU recently claimed 100,000 people will join Nigel Farage in a march against the High Court's ruling Parliament must have a say in triggering Article 50.
Plans of the protest emerged after Mr Farage warned of "political anger the like of which we have never seen in this country" if Britain's exit from the Eu was derailed.
Leave.EU said it planned to crowd fund £100,000 from its supporters to pay for barristers to represent the pro-Brexit argument in the court action.
If raised, Brexiteers would be able to challenge claims made by Remain and even the Government in court.
