Barack Obama has warned bluntly that Britain would be at "the back of the queue" for a trade deal with the US if it voted to leave the European Union.
In a far stronger intervention than expected, the US president urged British voters on Friday to back Remain in the 23 June referendum because otherwise the UK economy could be put at risk.
Obama insisted in a joint press conference with David Cameron he was "not coming here to fix any votes" and it was a "decision for the people of the United Kingdom".
The president said: "In democracies everybody should want more information, not less, and you shouldn't be afraid to hear an argument being made – that's not a threat, that should enhance the debate.
"Particularly because my understanding is that some of the folks on the other side have been ascribing to the United States certain actions we will take if the UK does leave the EU – they say for example that 'we will just cut our own trade deals with the United States'.
"So they are voicing an opinion about what the United States is going to do. I figured you might want to hear from the president of the United States what I think the United States is going to do.
"And on that matter, for example, I think it's fair to say that maybe some point down the line there might be a UK–US trade agreement, but it's not going to happen any time soon because our focus is in negotiating with a big bloc, the European Union, to get a trade agreement done.
"The UK is going to be in the back of the queue."
His no-holds-barred comments in the Foreign Office were welcomed by Cameron, who, amid fears of a low turnout among pro-EU voters, praised Obama’s “sage advice”.
The pair stood side by side to answer questions from journalists after an hour of bilateral talks in Downing Street. The president's three-day visit to London had provoked fury among some Conservative MPs, who accused him of hypocrisy for encouraging Britons to back the EU.
Leave campaigners dismissed Obama's warning. UKIP leader Nigel Farage pointed out that Obama will be out of office by the time Britain has extricated itself from the EU after a referendum.
Richard Tice, the co-founder of the Leave.EU campaign, added: "We don't have a trade deal with the United States now because we're members of the European Union. The proposed EU-US trade deal, TTIP, would be disastrous for British workers.
"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."
But Labour's Angela Eagle, the shadow business secretary, welcomed the president's comments. "Britain’s ability to negotiate trade deals would be hugely diminished after Brexit," she said.
"It is simply not credible for the Leave campaign to suggest we could swiftly negotiate a favourable trade deal with the United States and other countries."
Obama also responded to a controversial article by London mayor Boris Johnson in The Sun newspaper that claimed the president has an “ancestral dislike” of the British empire because he’s a “part-Kenyan president”.
Johnson, a prominent Leave campaigner, described how a bust of wartime leader Winston Churchill vanished from the Oval Office when Obama moved into the White House in 2009.
But Obama pointed out that while the bust had indeed been removed from that room – in favour of one of Martin Luther King – there was one of Churchill outside his private office on the second floor.
"Right outside the door of the Treaty Room, so that I see it every day, including on weekends when I'm going into that office to watch a basketball game, the primary image I see is a bust of Winston Churchill," the president said.
"It's there voluntarily because I can do anything on the second floor. I love Winston Churchill, I love the guy." While he didn't mention Johnson by name, Obama added: "I think people should know that, know my thinking there."
Cameron refused to get involved in the row, saying simply: "Questions for Boris are questions for Boris are questions for Boris."
Cameron said that for both the US and UK, "our collective power and reach is amplified by Britain's membership of the European Union".
He added: "When it comes to the special relationship between our two countries, there's no greater enthusiast than me.
"But I've never felt constrained in any way in strengthening this relationship by the fact that we are in the European Union. In fact, quite the reverse. "
The PM described Obama as "someone who gives sage advice, he's a man with a very good heart and he has been a very good friend – and always will be a good friend, I know, to the United Kingdom".
Obama insisted that whatever happened on the EU, the "special relationship" between Britain and the US would continue. He described how an aide wanted to come to Windsor with him to see the Queen, and how she had "almost fainted" when the monarch agreed to meet her.
"That's the special relationship," he said. "That will continue, hopefully eternally."
In a final pitch for Britons to back staying in the EU, the president added: "I think there's a British poet who said 'no man's an island', even an island as beautiful as this."