But the trip got off to a shaky start.
Romney openly doubted whether Britain could handle the games, saying it was unclear whether issues that have dogged the final preparations could be overcome.
"It's hard to know just how well it will turn out," Romney told NBC News in an interview on Wednesday, two days before the opening ceremonies.
Romney later met with Prime Minister David Cameron, and they discussed the Olympic Games in addition to alliances in Afghanistan and Syria.
"I expect the games to be highly successful," Romney declared after the meeting.
Earlier Thursday, Romney and Cameron seemed to address each other through the media. After Romney suggested it's impossible for any Olympic Games to go off without a hitch, Cameron said Romney and others will "see beyond doubt that Britain can deliver."
At the same time, Romney faced scrutiny for a London fundraiser Thursday night that's expected to attract employees of Barclays, which has been in the spotlight after becoming the first bank to admit its employees were involved in manipulating a key market index.
Last month, U.S. and British agencies fined Barclays a total of $453 million. In the wake of that shock, chief executive Bob Diamond resigned. Diamond had been scheduled to attend the fundraiser at the Mandarin Oriental hotel in the tony Knightsbridge district, but has pulled out. He already had sent Romney a check for $2,500.
Romney sought to steer the conversation away from the controversies.
"The world is a tumultuous and dangerous place," Romney said Thursday. "And certainly in many of the regions around the world we have great interests in having a common effort in seeing greater peace and prosperity."
As he met with British leaders past and present, the Republican also praised "the unique relationship that exists between our nations, our commitment to common values, our commitment to peace in the world and a desire to see a stronger and growing economy."
Romney, whose decades in private business gave him ample exposure to international affairs, is a former one-term governor untested on the world's political stage. He hopes to convince voters back home that he is no novice on foreign affairs and that they should feel confident electing him as president in a complex world and with the U.S. facing a myriad of security threats.
During the public portion of his meeting with Cameron, Romney weighed in again after his comment about the Olympics drew attention across Britain. "It is impossible for absolutely no mistakes to occur," he said. "Of course there will be errors from time to time, but those are all overshadowed by the extraordinary demonstrations of courage, character and determination by the athletes."
Meeting with British officials is typically one of the first priorities of any new president, and establishing those relationships beforehand can help smooth any transition. It's not unusual for American presidential candidates to meet with British leaders during the campaign; Obama did so when he took a trip abroad as the likely Democratic nominee in 2008.
Romney's weeklong trip also will take him to Israel and Poland.
On Thursday, Romney also met with former Prime Minister Tony Blair; Ed Miliband, the current leader of the Labour Party the opposition to Cameron's Conservative Party; and Foreign Secretary William Hague. The candidate also met with Nick Clegg, the deputy prime minister, and Chancellor of the Exchequer George Osborne, Britain's top financial official.
On Friday, Romney is scheduled to attend the opening ceremonies of the London Games.
This wasn't Romney's first meeting with Cameron; the two talked when Romney visited London in 2011. Cameron visited the U.S. earlier this year to meet with Obama and attended a White House state dinner, but he did not meet with Romney.
The meetings come a day after the Daily Telegraph published a story quoting an unidentified Romney campaign adviser saying the Republican believes the U.S. relationship with Britain is special because of shared "Anglo-Saxon heritage" that the adviser said the White House doesn't appreciate.
Romney, however, quickly distanced himself from any such view.
"I don't agree with whoever that adviser might be," Romney told NBC News, "but do agree that we have a very common bond between ourselves and Great Britain."
Nonetheless, Vice President Joe Biden and top Obama aides criticized Romney. "The comments reported this morning are a disturbing start to a trip designed to demonstrate Gov. Romney's readiness to represent the United States on the world's stage," Biden said.
Accompanying Romney to some of his meetings Thursday were former Missouri Sen. Jim Talent, an adviser, and Kerry Healey, who served as lieutenant governor when Romney was governor of Massachusetts. Three of Romney's sons Tagg, Josh and Craig also have joined him in London.