The US president's four-day trip -- perhaps his last to Britain before leaving office next year -- comes ahead of a June 23 referendum when Britons will be asked if they want to remain in the 28-member EU.
Obama is sure to be asked to weigh in on the issue during a joint press conference on Friday after talks with Prime Minister David Cameron or at a town hall-style meeting with British youngsters on Saturday.
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It may even come up at a lunch with Queen Elizabeth II at Windsor Castle on Friday -- a day after the monarch's 90th birthday, when the two heads of state will be joined by First Lady Michelle Obama.
Britain's departure from the EU -- so-called Brexit -- could have deep ramifications for Washington's "special relationship" with Britain, and on the stability of the European Union itself.
Obama has consistently said he favours a strong Britain in a strong EU.
Aides say he is likely to reinforce that message.
"I think his approach will be that if he's asked his view as a friend, he will offer it," said Ben Rhodes, one of Obama's closest foreign policy advisers.
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"But he'll make very clear that this is a matter that the British people themselves will decide when they head to the polls in June."
Privately, US officials are less reticent in their opinions as Britain's departure would deprive the United States of a key conduit for relations with Europe.
Seen from Washington, Cameron's decision to call a referendum was a bold -- if not downright risky -- gamble that could leave Britain and the EU badly weakened.
Polls put the pro-EU and Brexit camps neck-and-neck among those who express a preference to vote, although there is a large pool of people who remain undecided.
Cameron, the pro-EU campaign's figurehead, has been seriously embarrassed by revelations that he benefited from an offshore tax dodge.
His standing also took a blow when Obama suggested the prime minister had been too "distracted" to deal with the aftermath of the intervention in Libya.
Despite that apparent put-down, officials insist the two men enjoy a familiar and constructive working relationship.
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In public Obama has referred to the British PM as "bro," in stark contrast to more formal and standoffish relationship he has with many world leaders.
With Cameron facing a rebellion from within his own party over Europe, the prime minister will welcome any backing he can get.
But for Obama, wading in is not without risk.
Pro-Brexit supporters include popular London mayor Boris Johnson who has accused Obama of "outrageous and exorbitant hypocrisy" for his comments in favour of staying in the EU.
"I just think it's paradoxical that the United States, which wouldn't dream of allowing the slightest infringement on its own sovereignty, should be lecturing other countries," Johnson said on Tuesday.
Over 100 members of Britain's parliament have reportedly written to the American ambassador in London to make their displeasure known.
Even before Obama touches down, Britain's anti-EU crowd is clamouring to cast him as a meddling outsider.
That could be a potent argument in a country that shares cultural affinities with the United States, but which is deeply wary of being treated as America's lapdog.
The US president will thus have to tread a fine line as he seeks to amplify Cameron's argument in favour of EU membership.
Obama will likely stick to the big picture, said Jonathan Story, a professor at the INSEAD business school.
"What he will point out is that, after two US military interventions in Europe's wars, the US has a vital interest in the European project, just as it does in Japan's future, and the prosperity of Southeast Asia."
"A rising China and an unpredictable Russia are challenges enough... without the UK contributing to further disunion in Europe."
During Obama's visit he and the first lady will also have dinner on Friday with the Prince William, his wife Kate and brother Prince Harry.
From Britain he will travel to Germany for a meeting with German Chancellor Angela Merkel.
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