The president is expected to avoid areas where major demonstrations are planned in protest at his visit.
Ambassador Johnson sought to play down Trump's comments.
A helicopter took them from the airport to the USA ambassador's residence here.
Americans in London have been warned to "keep a low profile" during the trip, while a crowd-funded "Trump Baby" blimp has been cleared for take-off on Friday morning outside Parliament House. "If a balloon flying over London makes people laugh, I think that's absolutely worth it", she says.
Former House Speaker Newt Gingrich, the author of "Trump's America", said parallels can be drawn between Churchill's years in the wilderness during the 1930s and Trump's emergence in Republican politics from outside the establishment.
Tens of thousands of people are expected to march through London in protest against Mr Trump's visit and some of his actions during his first 18 months in power.
Protests are expected against Trump, whose policies - including a travel ban on a number of predominantly Muslim countries, the detention of child migrants on the US-Mexico border and the imposition of tariffs on European Union steel and aluminium exports - have all been criticised by the UK.
"I would love to say that I think this is going to be a hugely successful visit but I think it's going to be very hard", he said at a pro-Trump gathering in parliament.
Mr Trump and his wife Melania arrived at Stansted airport, where he was met by the UK's global trade secretary Liam Fox.
While it is not unusual for heads of state to visit Windsor Castle or meet the UK Prime Minister in her country home, it is quite unusual for an American president not to spend any time in London.
A high fence has been erected around the United States ambassador's central London residence where Trump will spend Thursday night and the embassy has sent out an alert warning Americans in London to keep a low profile in case protests turn violent.
A campaign is also underway to get "American Idiot", a 2004 song by the U.S. punk rock band Green Day, to the top of the UK Singles Chart.
Trump's wife is also concerned about how the British people will be viewing her and her husband during the trip. She said they will discuss security and defense, an aspect of the relationship that is causing anxiety for some British politicians.
He is due to stay overnight at the ambassador's Winfield House residence in London's Regent's Park, where demonstrators plan to play recordings of migrant children held in U.S. detention centers.
The two leaders will hold talks the following day at Chequers, the 16th-century manor house which is the prime minister's official country residence which will focus on Russian Federation, trade, Brexit and Middle East.