May appears to have seen off an immediate challenge to her leadership from malcontents within her Conservative Party but Trump's comments ahead of the trip - that Britain was "in somewhat turmoil" and that it was up to the people if she stayed in power - fanned the sense of political crisis.
"It's really kind of irrelevant to what we're trying to do and I don't think certainly it doesn't express the opinion of the British people I met", he said.
"There is no stronger alliance than that of our special relationship with the U.S. and there will be no alliance more important in the years ahead. That's certainly up to the people, not up to me", said Trump.
Speaking at an impromptu press conference after a North Atlantic Treaty Organisation summit in Brussels Trump said the British people shared his concerns on immigration, claiming "that's why Brexit happened". Trump himself noted the United Kingdom was "in turmoil" after the ministerial resignations it provoked.More news: Mandzukic sends Croatia to first World Cup final
Speaking to the Sunday Times, May said her husband was "looking forward to meeting Melania", adding that he "has been out and bought a new suit".
Security is still a cornerstone of the relationship, as are trade and less tangible things like shared language and the fact that many Americans are proud of their British roots.
And if London's National Air Traffic Service and Metropolitan Police Service decide at the last minute that for safety reasons, the balloon can not fly, this baby will be grounded.
His criticism of Britain's anti-terror policies after a series of attacks in 2017 also did not go down well. That prompted almost half a million people to sign a petition calling for Trump to be banned from the UK.More news: U.S. threatens nations over world breastfeeding resolution, shocking health officials
There are also plans for protestors to gather close to the U.S. ambassador's residence in Regent's Park, where Trump and his wife, Melania, will stay overnight on Thursday.
Russia, Brexit and the Middle East are set to top the agenda.
Trump's trip is part of a working visit and not a state visit, an invitation to which was extended to him personally by May just days after his inauguration. His late mother hailed from Scotland, where he owns two luxury golf courses.
May was the first head of government to officially meet Trump as president, in January 2017.More news: Croatia fans display banner in downtown Moscow
There will be small-scale protests all along Trump's itinerary and a mass demonstration called "Together Against Trump" by left-wing campaign groups in London on Friday.