The allegations centre around Vote Leave’s links to the BeLeave campaign which it helped fund.
Shahmir Sanni, who worked with Vote Leave, claims the group used BeLeave to get around strict spending limits set by the Electoral Commission.
It is a breach of electoral law for different campaign organisations to co-ordinate with each other unless they operate under a shared spending cap.
The campaign has strongly denied wrongdoing and said the £625,000 donated to BeLeave was within the rules.
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 has also accused senior Vote Leave figure Stephen Parkinson, now Theresa May’s political secretary, of “outing” him in a statement in which he disclosed the pair had been in a relationship for 18 months.
In that statement, Mr Parkinson said: “That is the capacity in which I gave Shahmir advice and encouragement, and I can understand if the lines became blurred for him, but I am clear that I did not direct the activities of any separate campaign groups.
“I had no responsibility for digital campaigning or donations during the referendum, and am confident that Vote Leave acted entirely within the law and strict spending rules at all times.”
Mr Sanni went to the Electoral Commission with two other pro-Brexit friends who claim they helped the Vote Leave campaign two years ago.
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.
He said: “There was no time where anything BeLeave did didn’t go through Stephen.”
In the final 10 days of the referendum campaign, Vote Leave donated £625,000 to Mr Grimes, who was registered as a permitted participant.
The money was used to pay Canadian data firm Aggregate IQ (AIQ), Channel 4 News reported.
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.”
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.”
Following the Channel 4 interview, Mr Parkinson said he was “saddened” by the “factually incorrect and misleading” statements by Mr Sanni and his lawyers.
He said: “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.”
Mr Grimes also denies all the allegations.
A Vote Leave spokesman said it had “twice been cleared on this matter by the Electoral Commission”.
Labour’s deputy leader Tom Watson said the allegations were “very serious”, adding: “The leaders of Vote Leave are senior cabinet ministers. We need answers about what really went on.”
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Liberal Democrat Brexit spokesman Tom Brake said: “These allegations must be examined by the police. If they represent what happened it is outrageous and shameful.”
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.”