But the Daily Mail reported Mr Trump has now cancelled a "working visit" to open the London embassy because he was unhappy about the arrangements and the scale of the trip.
The embassy says the new building was funded entirely by the proceeds of the sale of other US government properties in London, not through appropriated funds.
President Donald Trump says he has decided not to come to London to open the new U.S. Embassy, blaming the Obama administration for doing a "bad deal" to move the diplomatic mission.
"Vauxhall is a vibrant and important part of London and home to many businesses", May's spokesman Max Blain told reporters on Friday.
Mr Trump's decision not to visit was welcomed by critics outraged by the USA travel ban on some Muslim-majority countries, and more recently, his decision to re-tweet anti-Muslim videos posted by a British far-right organisation.
The embassy move from central London to a regenerated area on the south bank of the River Thames is in fact the result of a decade-long project initiated by the administration of former Republican president George W. Bush.
"Security concerns after 11 September meant we had to move to a location that could better protect American citizens and our British neighbours", Johnson wrote.
In January a year ago, Mrs May was the first foreign leader to visit Mr Trump in the White House.
MPs have repeatedly called for the offer of a state visit for the US President to be withdrawn following his crackdown on immigration from majority-Muslim countries and promotion of far-right group Britain First on Twitter.
Earlier this week, Foreign Secretary Boris Johnson had rejected suggestions that now was not the time for a state visit. Trump posted on social media platform Twitter.
"It appears that President Trump got the message from the many Londoners who love and admire America and Americans but find his policies and actions the polar opposite of our city's values of inclusion, diversity, and tolerance", Khan said in a statement.
The British government said the opening of the embassy was a matter for the United States. Mr Khan, a member of the main opposition Labour Party, said there would have been "mass peaceful protests", and that it was a "mistake" to invite him.
Mr Johnson tweeted at about 11am: "The US is the biggest single investor in the United Kingdom - yet Khan & Corbyn seem determined to put this crucial relationship at risk".
"Beyond the disagreements between leaders and the optics of this cancellation, U.S. -UK relations continue to remain strong - largely because there are a wide range of institutional ties between the nations in military cooperation, intelligence, economics, and commerce that operate as normal despite the political storms that may arise", Mahaffee said.