Mr Barzun told BBC Radio 4’s Desert Island Discs: “The tone in which it was said, there was nothing punitive about it.
“The point was, you are at the front of the queue right now – he [Obama] was saying back in April – because we are doing this big trade deal with the European Union, [the Transatlantic Trade and Investment Partnership (TTIP)] of which you are a member.
“But if you step out of the front of the queue, by definition you are no longer at the front, and some notion that you can jump further ahead: you just want to say that is not the trend for the types of big deals we are doing these days.”
Mr Barzun’s repeat of Mr Obama’s back-of-the-queue warning comes after the Vote Leave campaign went into the EU referendum insisting that Brexit would mean Britian gaining the power to strike its own trade deals.
Its website said: “We can speak for ourselves and sign new deals with countries all over the world, creating new jobs and new investment opportunities.”
This was despite the comments of Mr Obama when he visited Downing Street in April.
Mr Obama had said a post-Brexit, US-UK trade deal would be a long time coming – because America would focus first on big blocs such as the EU.
“It’s not going to happen any time soon,” Mr Obama said, “because our focus is on negotiating with a big bloc, the EU. The UK is going to be in the back of the queue.”
Mr Obama also advised the British electorate against voting to leave the EU, saying: “If, right now, I have got access to a massive market where I sell 44 per cent of my exports and now I'm thinking about leaving the organisation that gives me access to that market and that is responsible for millions of jobs in my country and responsible for an enormous amount of commerce and upon which a lot of businesses depend – that's not something I would probably do.”
Brexit campaigners dismissed the warning, however, with Nigel Farage accusing Mr Cameron of putting words in the US President’s mouth and Leave.Eu co-founder Richard Tice insisting: “Obama doesn’t have the authority to deny us a deal, as he will be long gone before any such proposals are on the table."
Mr Barzun, who helped orchestrate the grassroots campaign that was a key part of Mr Obama’s first presidential election victory in 2008, told Desert Island Discs that the President had felt compelled to warn about Brexit because of the special relationship between the UK and the US.
“We did what best friends do,” said Mr Barzun, 45. “So before the referendum when we were asked – and President Obama said it probably most forcibly – [we said] of course, it’s up to you but if you ask us, we will tell you what we think, which was: ‘We value a strong UK in a strong EU.’”
“What friends should do to each other,” he added, “is to be honest.”
But in the interview, which was broadcast today, Mr Barzun did also insist that the special relationship would survive Brexit.
“It sure is still special,” he told presenter Kirsty Young. “I think we are best friends, as it were, as countries.
“You think about the cultural, the commercial, the emotional and the intellectual connections between our countries. Those are unbreakable. Not unbreakable because they are some rigid thing. The opposite. They are unbreakable because they are flexible.”
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