Tillerson bucked tradition by not holding a formal meet-and-greet at the new embassy, which the State Department claimed was due to the current shutdown of the US government over a budget impasse in Congress.
But even before the shutdown, the State Department had already played down Tillerson’s visit to the embassy, which opened last week, due to controversy over Trump’s refusal to inaugurate the new building.
The president claimed it was because he was unhappy at the cost and location of the new embassy.
But the decision came after a series of rows that have damaged the so-called “special relationship” between the two nations and after it became clear the visit would be met with mass protests.
“The purpose of the trip is to underscore our commitment to the transatlantic alliance,” said a State Department spokesman.
“First stop is the United Kingdom, where the secretary will reaffirm the US-UK special relationship.”
Tillerson posed for photographs before being shown around the new building.
Trump had been due to inaugurate the building in February, but canceled the visit, tweeting: “having sold perhaps the best located and finest embassy in London for ‘peanuts,’ only to build a new one in an off location for 1.2 billion dollars. Bad deal. Wanted me to cut ribbon-NO!.”
The new building is slightly outside central London in a neighborhood south of the River Thames, unlike its predecessor, which was in the heart of the British capital.
Trump has not yet visited Britain since taking office a year ago, and has been involved in rows with the government over issues including trade and his retweeting of a video posted by a British far-right group.
London Mayor Sadiq Khan also said he “would not be welcome” in the city, suggesting there could be widespread protests.
Tillerson was to meet with Prime Minister Theresa May and Foreign Secretary Boris Johnson later in the day.
Johnson wrote in The Sunday Telegraph newspaper that Trump should be welcomed to Britain because the country’s ties with the US are vital for security and provide the UK’s “single most extraordinary economic relationship.”
Trump “is the elected president of the world’s most powerful democracy” and resisting his visit to the UK risks “damaging the national interest,” he added.
He and Tillerson are expected to discuss Yemen, Syria and the Iran deal.
During May’s meeting with Tillerson, the British premier was to say that London was “fully committed to the deal and also to working with our allies to counter Iran’s destabilising regional activity,” according to her spokesman.
Tillerson’s mini-tour of Europe will continue with a visit to Paris on Tuesday.