Two senior ministers resigned in protest this week at her plans for trade with the European Union after Britain leaves the bloc next March.
Melania and Mr Trump will arrive at Stansted airport on Thursday at midday after attending the North Atlantic Treaty Organisation summit in Brussels. "Now, for the benefit of all our people, let us work together to build a more prosperous future", she said.
In an interview with Britain's Sun newspaper published late on Thursday, Trump said May's plans for a business-friendly Brexit would leave it too close to the European Union to allow a new trans-Atlantic trade deal to be struck.
He said he got along with Theresa May "very well", but suggested he might make time during his United Kingdom visit to speak with his friend Boris Johnson, who has just rocked her Government by resigning as foreign secretary.
May is trying to unify her deeply divided Conservative Party behind her Brexit plans with some of her own lawmakers openly speaking of a leadership challenge.
May said there is "no stronger alliance" than the special relationship between the two countries and "there will be no alliance more important in the years ahead".
In another blow to May, Trump said her now ex-foreign secretary "would be a great prime minister".
Ahead of his arrival the PM said she would use the visit to "forge a strengthened, ambitious and future-proof trade partnership" with the U.S. after Brexit.
Many Britons are opposed to Trump's trip which is not the full state visit he was originally promised with the pomp and ceremony that entails.
Some 77 percent of Britons have an unfavorable view of Trump, according to a poll by YouGov with 1,648 respondents.
It has been a turbulent few weeks for America's US First Lady, who made jaws drop internationally in June while boarding a flight to visit a child detention centre wearing a jacket with: "I REALLY DON'T CARE, DO U?" emblazoned across the back of it.
After a weekend break in Scotland, they are expected to move on to Finland for Trump's much-hyped summit with Russian President Vladimir Putin in Helsinki on July 16.
He added there would be protests across the country against Trump's "abysmal record on human rights, his repugnant attitude towards women and his disgusting treatment of minorities".
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.
Tens of thousands of people are expected to protest against Trump's visit in central London on Friday, citing his alleged Islamophobia, controversial policies and "incendiary rhetoric" towards people with disabilities and the LGBTQ community.
A campaign is also underway to get "American Idiot", a 2004 song by the USA punk rock band Green Day, to the top of the UK Singles Chart.
The Trumps are joining Prime Minister May and other British business leaders at the black-tie dinner at the palace to kick off their visit to Britain.
On Friday, Trump will meet up again with May for a visit to an undisclosed military site before traveling to Chequers, her country estate, for talks on a range of issues.
Trade and security links, Brexit and the Middle East are among the issues to be discussed by Trump and May.