The Trumps left Winfield House at approximately 19:00 BST, with Mrs Trump wearing a full-length yellow dress with a pleated skirt.
Mr Trump, who will also spend time with the Queen during his two-day working visit, said earlier of the British public: "I think they agree with me on immigration... You see what's going on throughout the world with immigration... I think that's why Brexit happened."
He said "Brexit is Brexit" and the British people "voted to break it up, so I imagine that's what they'll do but maybe they're taking a different route - I don't know if that is what they voted for".
Mr Trump had joked earlier this week that his meeting with Vladimir Putin in the Finnish capital Helsinki on Monday "may be the easiest" part of his European trip.
Downing Street insisted Mrs May welcomed Mr Trump's decision to "engage" with the Russian leader.
But she also warned Mr Trump not to ignore the "malign behaviour" of Russia.
By James Landale, BBC diplomatic correspondent
Since Donald Trump took office, Theresa May has had to disagree with him publicly over his decision to impose trade tariffs on EU steel, abandon the Iran nuclear deal, move the US embassy to Jerusalem, order a Muslim travel ban and retweet anti-Muslim messages from a British far right group.
In turn, the US president has described Britain as being in political "turmoil", criticised its defence spending and shown no enthusiasm for coming to visit: in the 18 months of his presidency, Mr Trump has chosen to visit 17 other countries first.
Whatever this relationship is, it can hardly be described as special.
So this trip is about ticking a diplomatic box, getting a visit out of the way before its further delay became politically embarrassing.
And as working visits go, it is on the minimal side: no Downing Street barbecue, no cabinet visit, no speech to both Houses of Parliament.
The diplomatic aim will be to get through the visit without any gaffes, without upsetting the president, and without him saying anything disobliging about Brexit or a future trade deal.
The UK and the US do have a good relationship at an institutional level, in the fields of defence, security and intelligence. The tricky bit is always the politics and the personalities.
On Friday, Mrs May and Mr Trump will go to watch a joint counter-terrorism exercise by British and US special forces at a military base.
The pair will then travel to Chequers - the PM's country residence in Buckinghamshire - for talks with the foreign secretary.
The president and first lady will travel to Windsor on Friday afternoon to meet the Queen, before flying to Scotland to spend the weekend at Mr Trump's Turnberry golf resort. This part of the visit is being considered private.
The Police Federation has warned the visit will put "unquestionable pressure" on UK police forces as tens of thousands of people are expected to protest against the president in London on Thursday and Friday - and in Glasgow on Friday.