Anna Soubry has also said that failure to respond to concerns on the powderkeg issue was a “terrible, terrible mistake”, as it is widely seen to have swung the referendum in favour of leaving the EU.
The Small Business minster expressed fears about the prospect of Labour voters backing Brexit in large numbers but tells a BBC documetary that this fell on deaf ears.
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 tonight at 9pm on BBC Two.
“One of my colleagues had said they were very worried that it was all Project Fear and there should be more positivity and that was dismissed,” Ms Soubry said.
“I said on two occasions ‘I’m really worried bout the Labour vote.’ And it was, ‘yeah, whatever’.” 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.” First Minister Nicola Sturgeon and her predecessor Alex Salmond were among the senior political figures in Scotland who warned against a “Project Fear” approach from the Remain camp.
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.
Mr Corbyn, a previous critic of the EU, denied claims he did not play a full role in the Remain campaign.
Former Liberal Democrat leader Nick Clegg said former justice secretary Michael Gove was behind a controversial claim during the campaign that the Queen backed Brexit.
Buckingham Palace complained about the story which appeared in the Sun newspaper, claiming that the Queen had “let rip” at Mr Clegg about Europe at Windsor Castle. Mr Clegg said: “Michael Gove obviously communicated it well, I know he did.”
Mr Gove has previously denied briefing the story, which emerged in March.
Mr Clegg said: “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.”
Mr Clegg added; “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 the complaint.