On arrival in London, Trump and first lady Melania Trump headed for Winfield House, the residence of U.S. Ambassador to Britain Woody Johnson, where the Beatles song We Can Work It Out played outside.
Mr Smyth, who is originally from Ireland, said Trump fans had been given a bad rap, and there had been lots of support for the pub's temporary renaming. "I don't know [if] that is what they voted for", he added.
Asked about Trump's comments, May said: "We're delivering on the vote of the British people to take back control of our money, our laws and our borders".
Trump, who has repeatedly praised Brexit, has expressed enthusiasm for a wide-ranging trade deal with Britain after its European Union departure in March next year.
Trump has always been a Brexit supporter and has expressed enthusiasm for a wide-ranging trade deal with Britain after Brexit, something heralded by eurosceptics as being one of the great benefits of exiting the bloc.
Trump's victory in the 2016 presidential election shocked British diplomats in Washington and relations between May, a vicar's daughter, and Trump have been strained at times.
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.
We analyse his visit, trade, the special relationship and witness the pomp and ceremony.More news: Adam 'Pacman' Jones Fights & Knocks Out Airport Employee
Trump's remarks, made in a bombshell interview with The Sun published Thursday during his first visit to Britain as USA president, are an explosive intervention into British politics that seem likely to cause political chaos and imperil the prime minister as she attempts to negotiate Britain's exit from the European Union.
Some 77 percent of Britons have an unfavorable view of Trump, according to a poll by YouGov with 1,648 respondents.
Labour Party legislator Paul Flynn, who has criticized Mr. Trump in Parliament, says the USA leader has outraged Britons - and people around the world - with his harsh treatment of immigrants. "I think North Atlantic Treaty Organisation is much stronger now than it was two days ago".
His "America First" policies, including the decision to pull the United States out of the Paris climate accord and the nuclear deal with Iran, have brought him into conflict with Britain's leaders over issues of real substance.
A protest will also be held outside the president's Balmedie golf course in Aberdeenshire on Saturday, and it is expected there could be further demonstrations at his Turnberry resort in South Ayrshire. Reports have indicated that his visit will be met with protests, prompting a warning from the U.S. Embassy in London, which advised Americans in the country to "keep a low profile" in case the demonstrations turn violent.
May will seek to put the tensions behind her when she hosts Trump later Thursday for a black-tie dinner with business leaders at Blenheim Palace, the birthplace of World War II prime minister Winston Churchill.
On Friday, demonstrators are expected to gather near Chequers, the Prime Minister's country residence, where May and Trump will hold a working lunch.