US President Barack Obama defended his appeal to British voters to stay in the European Union on Friday, saying the "special relationship" between the two nations means he was acting as a "best friend."

"I'm offering my opinion. In democracies, everyone should want more information, not less," Obama said after eurosceptic critics accused him of interfering in the debate ahead of a referendum on Britain's EU membership on June 23.

"If one of our best friends is in an organization that enhances their power, enhances their economy ... I want them to stay in it," he told reporters at a joint press conference after talks with British Prime Minister David Cameron, who is campaigning to remain in the EU.

Obama warned that a vote to leave the EU could put Britain "in the back of the queue" for negotiating a bilateral trade deal with the United States, as Washington prioritizes an agreement with the EU.

Cameron defended Obama's right to speak in Britain on the referendum, saying he had made comments on previous US elections.

"I think it's right to listen to, and consider, the views of your friends," he said.

"When it comes to the special relationship between our countries, there's no greater enthusiast than me," Cameron said.

"But I've never felt constrained in this relationship by the fact that we're in the European Union," he said.

Obama paid tribute to Cameron as "one of my closest and most trusted partners."

"As David says, this [EU membership] magnifies the power of the UK, it doesn't diminish it," Obama said. "It enhances the special relationship, it doesn't diminish it."

Obama also praised Queen Elizabeth II is "one of my favourite people," confirming that his visit to Britain is timed to coincide with her 90th birthday.

"She's truly one of my favourite people," Obama said. "She's an astonishing person and a real jewel to the world, not just to the United Kingdom."

"Earlier today, Michelle and I had the honour to join Her Majesty and His Royal Highness, the Duke of Edinburgh, as their guests at Windsor Castle, where we conveyed the good wishes of the American people," he said, following a private lunch at the royal residence outside London.

The Obamas had a "very smooth ride" in a Range Rover driven by Prince Philip, the 94-year-old Duke of Edinburgh, as they travelled from their helicopter to the door of Windsor Castle, he said.

Obama and Cameron said they discussed Libya, Syria, the fight against Islamic State and other international issues.

The US leader's arrival in London was overshadowed by a row over his intervention on the EU referendum.

Writing in The Telegraph, Obama appealed to British voters to stay in the European Union, telling them the United States "needs your influence to continue" and arguing that Britain's security and economic growth would be better if it remained part of the EU.

"The United States sees how your powerful voice in Europe ensures that Europe takes a strong stance in the world, and keeps the EU open, outward looking, and closely linked to its allies on the other side of the Atlantic," he wrote.

"So the US and the world need your outsized influence to continue - including within Europe," Obama said.

He stressed the EU's role in pursuing a nuclear deal with Iran and the Paris climate agreement, and he also addressed the key economic debate for and against Brexit.

Campaigners for a Brexit, or British exit from the EU, criticized his intervention. Iain Duncan Smith, a leading eurosceptic in Cameron's Conservative Party, accused the US president of trying to "intimidate the British people into voting to stay in the EU."

Writing in The Sun, London Mayor Boris Johnson, another Conservative backer of Vote Leave, called Obama's appeal to Britain "a breathtaking example of the principle of 'do as I say, but not as I do.'"

Critics slammed Johnson after he claimed the White House could have removed a bust of British wartime prime minister Winston Churchill because of the "part-Kenyan" president's "ancestral dislike of the British empire."

Asked about Johnson's remarks during the joint press conference, Cameron declined to comment.

The Obamas later travelled to London's Kensington Palace, where they dined with Prince William and his wife, Kate, and their young son, Harry.

On Saturday, the president is to host a "town hall" question-and-answer event in London and attend a dinner with Cameron.

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