Following an investigation, the Electoral Commission found that Vote Leave and Darren Grimes, a campaigner who founded a group called BeLeave, coordinated their campaigns to allow the official Brexit campaign to avoid its £7m spending limit.
Mr Grimes and David Halsall, the ‘responsible person’ at Vote Leave, have both been referred to the Metropolitan Police.
The Scottish Government's Brexit Secretary Michael Russell tweeted that the findings were "damning" and meant it was "essential" to hold a new vote on EU membership.
BeLeave spent more than £675,000 with the same online data company, Aggregate IQ, as Vote Leave in what the Electoral Commission has concluded was a “common plan”. Separate campaigns are not allowed under law to work closely together and direct spending under a coordinated strategy.
Mr Grimes has been fined £20,000 - the highest possible fine - for two offences, including breaching BeLeave’s £10,000 by nearly £666,000. Vote Leave has been fined £6,100.
Bob Posner, the Electoral Commission’s director of regulation and legal counsel, said Vote Leave “refused to cooperate” with the investigation.
“The Electoral Commission has followed the evidence and conducted a thorough investigation into spending and campaigning carried out by Vote Leave and BeLeave,” he said.
“We found substantial evidence that the two groups worked to a common plan, did not declare their joint working and did not adhere to the legal spending limits.
“These are serious breaches of the laws put in place by Parliament to ensure fairness and transparency at elections and referendums.”
Mr Posner added: “Vote Leave has resisted our investigation from the start, including contesting our right as the statutory regulator to open the investigation.
“It has refused to cooperate, refused our requests to put forward a representative for interview, and forced us to use our legal powers to compel it to provide evidence.
“Nevertheless, the evidence we have found is clear and substantial, and can now be seen in our report.”
The Electoral Commission added that the legal limit for fines under electoral law of £20,000 is "inadequate for serious offences of electoral or referendum law".