London (CNN) With flattery, poetry, and a blatant threat, President Barack Obama on Friday urged British voters to remain in the European Union -- a controversial intervention into the referendum debate rocking America's closest ally.

Obama rejected claims by anti-Europe campaigners that he was interfering in internal U.K. politics, and in a serious blow to the "Leave" campaign, warned Britain not to bank on a free trade deal with Washington if it quits the EU.

In perhaps the most significant moment in the referendum campaign so far, the U.S. President, taking advantage of his popularity in the United Kingdom, spoke with greater frankness about the possibility of a so-called "Brexit" than expected. He argued that a British departure from the alliance would not just be bad for the United Kingdom, but would run contrary to the national interests of the United States, threatening stability and prosperity in the Western world at a time of turmoil.

"Let me be clear, ultimately this is something that the British voters have to decide for themselves," Obama said at a news conference alongside David Cameron, delivering a boost to the British Prime Minister's bid to safeguard U.K. membership in the EU.

"But as part of our special relationship, part of being friends, is to be honest and to let you know what I think," Obama said.

"Speaking honestly, the outcome of that decision is a matter of deep interest to the United States because it affects our prospects as well," Obama said, and also hinted that the U.K. would be a less valuable ally to Washington if it left the bloc.

"The United Kingdom is at its best when it is helping to lead a strong Europe. It leverages UK power to be part of the European Union," Obama said.

"I think there is a British poet who said: 'No man is an island' — even an island as beautiful as this," Obama said, quoting a beloved poem by John Donne, a contemporary of William Shakespeare.

Seeking to convince Britons of his arguments, the President also deployed flattery, paying warm tribute to their country's role as a world leader and said it still had an outsized contribution to make. He also lavished praise on Queen Elizabeth II, with whom he and his wife Michelle had lunch at Windsor Castle, saying she was a source of "inspiration."

But behind the compliments was a steely argument that infuriated campaigners who see the June referendum as a chance to reclaim British sovereignty from Brussels, to strengthen U.S. borders amid a European migration crisis and to free U.K. businesss of continental regulations.

One of Britain's most famous and flamboyant political figures backing the "Leave" movement -- London mayor and cabinet member Boris Johnson -- warned in an opinion article in "The Sun" newspaper that Obama's arguments were "incoherent," "inconsistent" and "downright hypocritical."

"The Americans would never contemplate anything like the EU, for themselves or for their neighbours in their own hemisphere. Why should they think it right for us?" Johnson wrote, also accusing Obama of snubbing Britain by removing a bust of war time prime minister Winston Churchill from the Oval Office in 2009.

But Obama hit back.

"I am not coming here to fix any votes, I am not casting a vote myself, I am offering an opinion," he said. "In democracies, everybody should want more information, not less."

He went on: "That is not a threat -- that should enhance the debate."

And the President scoffed at the long-running saga of the Churchill bust, which has frequently been used as a cudgel against him by political opponents in Washington and London. He said that for the last seven years, the piece has sat outside his private office in the White House residence, and that as the first African-American president, he wanted to have a bust of civil rights icon Martin Luther King, Jr., in the Oval Office.

"I love Winston Churchill. I love the guy," Obama said.

Photos: Obama visits Saudi Arabia, UK and Germany Photos: Obama visits Saudi Arabia, UK and Germany From left, British Prime Minister David Cameron, Italian Prime Minister Matteo Renzi, U.S. President Barack Obama, German Chancellor Angela Merkel and French President Francois Hollande sit together at Herrenhausen Palace in Hanover, Germany, on Monday, April 25. Germany was the third stop on Obama's recent trip, which also included the United Kingdom and Saudi Arabia. Hide Caption 1 of 19 Photos: Obama visits Saudi Arabia, UK and Germany Obama and Merkel look at a robotic device April 25 as they tour the Hannover Messe, the world's largest trade fair for industrial technology. Hide Caption 2 of 19 Photos: Obama visits Saudi Arabia, UK and Germany Obama tests virtual reality goggles at the Hannover Messe on April 25. Hide Caption 3 of 19 Photos: Obama visits Saudi Arabia, UK and Germany Obama and Merkel look at a gripping device at the Hannover Messe on April 25. Hide Caption 4 of 19 Photos: Obama visits Saudi Arabia, UK and Germany From left, U.S. Secretary of Commerce Penny Pritzker, Obama and Merkel attend the opening ceremony of the Hannover Messe on Sunday, April 24. Hide Caption 5 of 19 Photos: Obama visits Saudi Arabia, UK and Germany Obama and Merkel hold a news conference after bilateral talks at Herrenhausen Palace on April 24. Hide Caption 6 of 19 Photos: Obama visits Saudi Arabia, UK and Germany Merkel welcomes Obama at Herrenhausen Palace on April 24. Hide Caption 7 of 19 Photos: Obama visits Saudi Arabia, UK and Germany Obama speaks at a news conference in London on Saturday, April 23. Hide Caption 8 of 19 Photos: Obama visits Saudi Arabia, UK and Germany British Prime Minister David Cameron and Obama play golf at the Grove Golf Club on April 23. Hide Caption 9 of 19 Photos: Obama visits Saudi Arabia, UK and Germany Obama takes a brief tour of the Globe Theatre in London with Patrick Spottiswoode, director of Globe Education, marking the 400th anniversary of the death of William Shakespeare on April 23. Hide Caption 10 of 19 Photos: Obama visits Saudi Arabia, UK and Germany Obama, Prince William and first lady Michelle Obama talk with Prince George at Kensington Palace on Friday, April 22. Hide Caption 11 of 19 Photos: Obama visits Saudi Arabia, UK and Germany Queen Elizabeth II and her husband, Prince Philip, greet Obama outside Windsor Castle on Friday, April 22. Hide Caption 12 of 19 Photos: Obama visits Saudi Arabia, UK and Germany A motorcade drives the Obamas to Windsor Castle for lunch with Queen Elizabeth II on April 22. Hide Caption 13 of 19 Photos: Obama visits Saudi Arabia, UK and Germany Obama arrives at Downing Street to meet with Cameron on April 22. The American leader is urging British voters to reject the chance to leave the European Union in a national referendum scheduled for June. Hide Caption 14 of 19 Photos: Obama visits Saudi Arabia, UK and Germany Before Britain, Obama met with Oman's Deputy Prime Minister Sayyid Fahad Mahmoud Al Said, left, and Saudi King Salman at the Gulf Cooperation Council summit, which took place Thursday, April 21, in Riyadh, Saudi Arabia. Obama spoke with Gulf leaders about regional conflicts, the role of Iran and the fight against ISIS. Hide Caption 15 of 19 Photos: Obama visits Saudi Arabia, UK and Germany Obama confers with other leaders at the Gulf Cooperation Council summit on April 21. Hide Caption 16 of 19 Photos: Obama visits Saudi Arabia, UK and Germany The United States and Saudi Arabia have been divided over a slew of issues, including the approach to the wars in Syria and Yemen, the Iranian nuclear deal and the influence Tehran wields in Iraq. Here, Obama appears with Saudi King Salman, Bahrain's King Hamad bin Isa Al Khalifa and Abu Dhabi Crown Prince Mohamed bin Zayed Al Nahyan during the Riyadh summit on April 21. Hide Caption 17 of 19 Photos: Obama visits Saudi Arabia, UK and Germany Obama and Saudi King Salman meet at Erga Palace in Riyadh on Wednesday, April 20. The White House moved to tamp down suggestions that ties with Saudi Arabia are fraying, with administration officials saying the two leaders "really cleared the air" in their meeting. Hide Caption 18 of 19 Photos: Obama visits Saudi Arabia, UK and Germany Obama arrives on Air Force One at King Khalid International Airport in Riyadh on April 20. Saudi King Salman did not greet the President on his arrival. The perceived slight was seen as one more sign that the U.S.-Saudi relationship is encountering friction. Hide Caption 19 of 19

In the most significant policy exchange of the hour-long news conference, Obama inflicted a serious blow on the "Leave" campaign, which maintains that Britain could make up for the loss of tariff-free access to European markets by quickly sealing a free trade deal with the United States.

"The U.K. is going to be in the back of the queue," Obama said, pointing out that the United States was already working on concluding a free trade agreement with the European Union itself, noting that in the current political environment negotiating such deals was a heavy lift.

"I think it is fair to say that maybe some point down the line, there might be a U.K.-U.S. trade agreement but it is not going to happen any time soon," Obama said.

The President also warned that divisions that could be fostered in Europe by a British exit could hurt the collective security of the United States and the continent and could harm NATO. And he said he wanted the British Prime Minister to be in the room when key decisions were made: "I want one of my strongest partners in that conversation."

Cameron, with one eye on the furor whipped up by Obama's intervention in the Europe debate, praised the U.S. leader as a personal friend, and as a friend of Britain who often offered sage advice. And he said that there was no contradiction in Britain having a strong "special relationship" with the United States and taking a leadership role in the European Union.

"I have never felt constrained in any way in straightening this relationship by the fact we are in the European Union -- in fact quite the reverse," Cameron said, adding Britain's power and reach was enhanced by its membership in the European bloc.

Obama and Cameron also spoke during their meeting in 10 Downing Street about other challenges facing Europe and the West, including the refugee exodus from the Middle East and the need for NATO members to meet their spending commitments.

In a recent interview with "Atlantic" magazine, Obama complained about "free riders" in Europe and faulted Cameron for taking his eye off of the need to build a functioning state in Libya after a NATO intervention in 2011.

The two leaders also hoped to plot an effective plan to retake Mosul, in northern Iraq, where ISIS has been in control for almost two years. The U.S. has been working to develop the Iraqi military with the goal of liberating the city, but political concerns in Iraq's central government have led to questions about the effectiveness of the fighting forces.

Obama will reiterate his bid for greater cooperation during a visit to Germany on Sunday, where he'll meet with European allies, including Cameron, along with German Chancellor Angela Merkel, Italian Prime Minister Matteo Renzi and French President Francois Hollande.

On that trip, he is also expected to make a long distance case to Americans about the need to preserve the U.S. relationship with Europe, following warnings by Republican presidential front-runner Donald Trump that the transatlantic alliance is costing America too much money and not delivering sufficient results.

Cameron, who has previously condemned some of Trump's controversial remarks, was asked to weigh in on the campaign, following reports that the prospect that the real estate mogul could win the White House is triggering panic around the world.

He said he would not elaborate on his prior remarks but would not "subtract" from them either.