The claims centre around Vote Leave’s links to another campaign - BeLeave - which it helped fund.
Shahmir Sanni, who worked on the campaign, claimed Vote Leave used it to get around strict spending limits set by the Electoral Commission.
Vote Leave has strongly denied wrongdoing and said the £625,000 donated to BeLeave was within the rules.
But Mr Sanni told Channel 4 News: “I know that Vote Leave cheated ... I know that people have been lied to and that the referendum wasn’t legitimate.”
Mr Sanni was in a relationship with senior Vote Leave figure Stephen Parkinson - now Theresa May’s political secretary - at the time of the referendum and claimed through his lawyers he was “outed” by the Number 10 aide in the run-up to the Channel 4 disclosure.
Mr Sanni went to the Electoral Commission with two other pro-Brexit friends on Thursday, who say they helped the Vote Leave campaign two years ago, Channel 4 reported.
Their lawyers have given the election watchdog signed statements.
Mr Sanni told the broadcaster he was initially a Vote Leave outreach volunteer but he was then assigned to BeLeave.
Vote Leave said it did not recall Mr Sanni working as a volunteer, but he was “like hundreds of others who occasionally visited the offices”.
Mr Sanni said that he and BeLeave’s co-founder Darren Grimes always reported to Mr Parkinson.
“There was no time where anything BeLeave did didn’t go through Stephen,” he said.
In the final 10 days of the 2016 referendum campaign Vote Leave donated £625,000 to Mr Grimes, who was registered as a permitted participant, with the money used to pay Canadian data firm Aggregate IQ (AIQ), the programme said.
Asked whether they could have refused to spend the money on AIQ, Mr Sanni said: “We didn’t ever feel like we had that level of control.
“That’s what I mean, we never felt like we had control over the organisation itself.”
He claimed: “In effect they used BeLeave to over-spend, and not just by a small amount ... Almost two-thirds of a million pounds makes all the difference and it wasn’t legal.”
Mr Parkinson said he was “saddened” by the “factually incorrect and misleading” statements by Mr Sanni and his lawyers.
He added: “At the relevant time during the referendum period, the commission advised Vote Leave that it was permissible to make a donation in the way it proposed to do to BeLeave.
“Twice since the referendum the commission has investigated this matter, and twice it has found no evidence of wrongdoing. A third investigation into the same issue is currently taking place.
“The Electoral Commission has not contacted me in relation to any of these inquiries, but I will of course be happy to assist in them if they wish me to do so.
“I firmly deny the allegations in the programme.
“I had no responsibility for digital campaigning or donations on the Vote Leave campaign, and am confident that I stayed within the law and strict spending rules at all times.”
Mr Grimes also denies all the allegations, Channel 4 said.
A Vote Leave spokesman said it had “twice been cleared on this matter by the Electoral Commission” adding: “There are now a number of new accusations and allegations.
“While many of them seem irrelevant or trivial, some are serious and potentially damaging to the reputations of those caught up in those allegations.
“As has been the case throughout, Vote Leave is obligated to review - to the extent it can after this long elapsed period since the referendum - all such allegations, and is doing so.
“We will as appropriate share any relevant findings with the Electoral Commission, again as we have always done.”
An Electoral Commission spokeswoman said: “The commission has a number of investigations open in relation to campaigners at the EU Referendum; it does not comment on live investigations. “