Former deputy PM Nick Clegg has told the BBC that Michael Gove was behind the Sun's "Queen Backs Brexit" story.
The Palace complained about the story, which quoted an anonymous source as saying the Queen had "let rip" at Mr Clegg about Europe at Windsor Castle.
Mr Clegg told a BBC documentary on Brexit that "Michael Gove obviously communicated it - well, I know he did".
Mr Gove has previously denied briefing the story, which ran in March, and the Sun has said it had two sources.
Former Justice Secretary Mr Gove has said: "I don't know how the Sun got all its information and I don't think it's really worth my adding anything to what's already been said."
'It didn't happen'
Key figures from both sides of the campaign in the EU referendum spoke to BBC political editor Laura Kuenssberg for the documentary Brexit: The Battle for Britain, which runs on Monday at 21:00 BST on BBC Two.
Mr Clegg said: "I mean, the idea that the Queen of all people would even bother to give someone as insignificant as a 'here today, gone tomorrow' deputy prime minister a tongue lashing about Europe I just think is... so preposterous, so it was not true... I think it was very, very disrespectful of Michael Gove to have done that."
The Independent Press Standards Organisation (Ipso) ruled the headline had been inaccurate, following a complaint from Buckingham Palace. The Sun stood by the story.
Meanwhile, Anna Soubry - who was a business minister - told the documentary that the Remain camp's failure to focus on immigration, which was a main focus for the Leave campaign, was a "terrible, terrible mistake".
She added: "We did fear on the economy, keep on about the economy... which was right, but not all the way over it because people got bored and tired with that.
"It was like we kind of made and won that argument, so then the vacuum appeared and then bang, in they came with their killer card, which was immigration and we refused to engage in it."
By Chris Mason, BBC political correspondent
Losing political campaigns often resemble a circular firing squad. Such and such was the turning point, why on earth didn't we say this, why did we bang on about that?
But two things stand out a mile watching Laura's documentary.
It is a reminder, as if we needed it, of the magnitude of what happened in June.
And it is a reminder too of how that circular firing squad, in this instance, is the towering heights of the establishment: big business, the leadership of the big political parties, and leading figures in the arts and sport too.
Despite - or perhaps because - of everything they said, they lost.
And the ramifications of that on our politics will last a very long time.
The divide in views amongst Conservative ministers also features in the programme. Craig Oliver - the ex-Number 10 director of communications who was knighted in David Cameron's resignation honours - told the programme the prime minister only found out senior Conservative MP and then London Mayor Boris Johnson was to campaign to leave the EU 15 minutes before his public announcement.
He said there had also been "a moment of surprise" when Mr Cameron realised his cabinet colleague Mr Gove was to chair the Vote Leave campaign.
Mr Gove had "given the impression that he would not play a very significant role" in the campaign, Mr Oliver told the programme.
He said it was "naive" to suggest the government had not needed to call the referendum, adding: "You could either deal with it now or the reality is it would pop up again in a few months, or a few years."
Meanwhile, Will Straw, who headed the Britain Stronger In Europe campaign, told the programme it had taken six months to get a meeting with one of Labour leader Jeremy Corbyn's advisers.
"They did not want to work with us, despite the fact that I'd been a candidate for the Labour Party at the 2015 election," said Mr Straw.
Asked what he thought Mr Corbyn's attitude to the UK's EU membership was, Mr Straw added: "He was lukewarm about it."
Labour peer Lord Mandelson also accused Mr Corbyn of undermining the campaign to keep Britain in the EU.
He said the Labour In campaign felt its efforts were at times "undermined" and "sabotaged" by Mr Corbyn and those around him, adding that it was "very difficult" to know what the Labour leader's motives were.
Mr Corbyn has rejected criticisms that he had not been in the vanguard of the referendum campaign.
He told an audience at a hustings debate on Thursday, against his leadership challenger Owen Smith: "We spent a lot of money on it, we did a lot of campaigning.
"I travelled the whole country doing a very large number of meetings."
Gisela Stuart, the Labour MP who co-chaired the Vote Leave campaign, told the programme she believed an "unravelling of the Labour heartlands not feeling that the Labour Party was representing them" was a "real problem" for the Remain side.
"The minute you left the M25 ring, there was a real groundswell of people who wanted to leave, which was something the metropolitan liberal elite simply had not recognised.
"People were coming up and it was like revealing an unpleasant secret: 'You know, I'm voting Leave and even worse, I'm a Labour Party member and I'm voting Leave'."