London (CNN) After two-and-a-half years of unsteady dealings and the occasional insult, President Donald Trump offered a deeply gracious send-off for Prime Minister Theresa May on Tuesday, their final interaction before May steps aside amid a paralyzing debate over Brexit.

It was an uncharacteristically courteous display from a President who a day earlier was insulting London's mayor from his plane and griping about negative coverage of his state visit here.

Twenty-four hours later, Trump appeared charmed by the overt displays of flattery on offer by Britain's royal family and members of the government, deeming Queen Elizabeth II a "fantastic person" and hailing the long-established special transatlantic relationship.

Trump weighs in

While he professed to be wary of taking opinions on Britain's internal matters, Trump predicted Brexit would and should happen -- and said May had "brought it to a very good point where something will take place in the not too distant future."

"I think she's done a very good job," Trump said, reversing past critiques of her failure to strike a deal that both Parliament and the EU can accept.

"This is a great, great country and it wants its own identity," Trump said. "It wants to have its own borders. It wants to run its own affairs. This is a very, very special place and I think it deserves a special place."

Still, for all his praise of May, Trump did not hide his enthusiasm for some of the men who may replace her, even those who have been sharply critical of May's handling of Brexit.

He said Boris Johnson, the former London mayor who resigned in protest from May's cabinet, "would do a very good job" as prime minister. Earlier in the day, Trump phoned Johnson and offered a one-to-one meeting, according to a British official. Johnson thanked the President for the invitation, but declined the meeting to focus on a political event that was happening at the same time, the official said.

Trump also offered praise for foreign secretary Jeremy Hunt, another contender to replace May. And though he claimed not to know Michael Gove, the environment minister and a third possible candidate, he was assured that he, too, would suffice as prime minister.

Photos: In pictures: President Trump in Europe US President Donald Trump, visiting the Normandy American Cemetery in France, participates in a ceremony to commemorate the 75th anniversary of D-Day on Thursday, June 6. Hide Caption 1 of 45 Photos: In pictures: President Trump in Europe Trump and his wife, Melania, visit the graves of troops who died on D-Day. Hide Caption 2 of 45 Photos: In pictures: President Trump in Europe The Trumps are joined by French President Emmanuel Macron and his wife, Brigitte, as they watch a flyover on June 6. Hide Caption 3 of 45 Photos: In pictures: President Trump in Europe A World War II veteran shows Trump a photo of himself with the President. Hide Caption 4 of 45 Photos: In pictures: President Trump in Europe Trump addresses the commemoration ceremony in France. Hide Caption 5 of 45 Photos: In pictures: President Trump in Europe Macron and Trump embrace during the D-Day ceremony. Hide Caption 6 of 45 Photos: In pictures: President Trump in Europe A World War II veteran looks over Trump's shoulder during the commemoration ceremony. Hide Caption 7 of 45 Photos: In pictures: President Trump in Europe At a D-Day event held Wednesday, June 5, in Portsmouth, England, Trump reads a prayer that President Franklin D. Roosevelt gave over the radio on D-Day. Hide Caption 8 of 45 Photos: In pictures: President Trump in Europe Trump heads back after speaking at the event in Portsmouth on June 5. Hide Caption 9 of 45 Photos: In pictures: President Trump in Europe Britain's Queen Elizabeth II and Prince Charles play host to the Trumps at the D-Day event in Portsmouth. British Prime Minister Theresa May is at left. Hide Caption 10 of 45 Photos: In pictures: President Trump in Europe Trump meets with German Chancellor Angela Merkel on the sidelines of the D-Day event in Portsmouth. Hide Caption 11 of 45 Photos: In pictures: President Trump in Europe The Trumps pose for a photo ahead of a dinner at Winfield House in London on Tuesday, June 4. Joining them, from left, are Woody Johnson, the US ambassador to the United Kingdom; Camilla, the Duchess of Cornwall; Prince Charles; and Johnson's wife, Suzanne Ircha. Hide Caption 12 of 45 Photos: In pictures: President Trump in Europe Trump and Prince Charles share a toast at Winfield House. Hide Caption 13 of 45 Photos: In pictures: President Trump in Europe Trump and British Prime Minister Theresa May speak at the dinner on June 4. Hide Caption 14 of 45 Photos: In pictures: President Trump in Europe Melania Trump spends time with Camilla and Suzanne Ircha, the wife of the US ambassador. Hide Caption 15 of 45 Photos: In pictures: President Trump in Europe Brexit Party leader Nigel Farage, center, arrives at Winfield House, where the Trumps are staying during their visit. Hide Caption 16 of 45 Photos: In pictures: President Trump in Europe Trump and May give a joint news conference on June 4. "I think she's done a very good job," Trump said, reversing past critiques of her failure to strike a Brexit deal that both Parliament and the EU can accept. Hide Caption 17 of 45 Photos: In pictures: President Trump in Europe Trump and May are followed by their spouses as they make their way to the news conference in London on June 4. The President offered plenty of praise for May, who recently announced her resignation. Hide Caption 18 of 45 Photos: In pictures: President Trump in Europe Philip May and Melania Trump attend a garden party at No. 10 Downing Street. Hide Caption 19 of 45 Photos: In pictures: President Trump in Europe Larry, the No. 10 Downing Street cat, sits underneath The Beast, the presidential armored Cadillac. Hide Caption 20 of 45 Photos: In pictures: President Trump in Europe Trump speaks opposite May at a business roundtable discussion in London. Hide Caption 21 of 45 Photos: In pictures: President Trump in Europe Trump stands next to Queen Elizabeth II before a state banquet at Buckingham Palace on Monday, June 3. Joining them are Melania Trump, Prince Charles and Camilla. Hide Caption 22 of 45 Photos: In pictures: President Trump in Europe The state banquet had a few hundred guests, including several of Trump's children. Hide Caption 23 of 45 Photos: In pictures: President Trump in Europe Trump and the Queen laugh during the state banquet. Hide Caption 24 of 45 Photos: In pictures: President Trump in Europe The Trumps tour Westminster Abbey on June 3. Hide Caption 25 of 45 Photos: In pictures: President Trump in Europe The President signed the guestbook at Westminster Abbey. "Thank you so much," his message said. "This has been a great honor. Special place." Hide Caption 26 of 45 Photos: In pictures: President Trump in Europe The Trumps are joined by Prince Andrew as they pay their respects at the Tomb of the Unknown Warrior in Westminster Abbey. Hide Caption 27 of 45 Photos: In pictures: President Trump in Europe The President's convoy drives down Pall Mall in London on June 3. Hide Caption 28 of 45 Photos: In pictures: President Trump in Europe Queen Elizabeth II welcomes the Trumps to Buckingham Palace. She took them on a tour of the royal collection. Hide Caption 29 of 45 Photos: In pictures: President Trump in Europe Among the items on display was "American Pewter Thoroughbred," a gift that Trump gave the Queen last year. Hide Caption 30 of 45 Photos: In pictures: President Trump in Europe Trump inspects a guard of honor at Buckingham Palace. Hide Caption 31 of 45 Photos: In pictures: President Trump in Europe The US National Anthem is played during a welcoming ceremony at Buckingham Palace. From left are Melania Trump, the Queen, Trump, Charles and Camilla. Hide Caption 32 of 45 Photos: In pictures: President Trump in Europe British Army troops fire a cannon in London's Green Park to mark the beginning of Trump's visit. Hide Caption 33 of 45 Photos: In pictures: President Trump in Europe The Queen greets the President as he arrives at Buckingham Palace. Hide Caption 34 of 45 Photos: In pictures: President Trump in Europe Prince Charles greets Trump as he steps off Marine One at Buckingham Palace. Hide Caption 35 of 45 Photos: In pictures: President Trump in Europe The Trumps are welcomed in London by Charles and Camilla. Hide Caption 36 of 45 Photos: In pictures: President Trump in Europe Trump's daughter Ivanka, who is also advisor to the President, looks out of a window at Buckingham Palace. Hide Caption 37 of 45 Photos: In pictures: President Trump in Europe People outside Buckingham Palace photograph the Changing of the Guard ahead of Trump's arrival on June 3. Hide Caption 38 of 45 Photos: In pictures: President Trump in Europe The Trumps arrive at Winfield House, the residence of the US ambassador, on June 3. Hide Caption 39 of 45 Photos: In pictures: President Trump in Europe Amnesty International installs "Resist Trump" banners on Vauxhall Bridge in London. Hide Caption 40 of 45 Photos: In pictures: President Trump in Europe Marine One flies past the BT Tower in London. Hide Caption 41 of 45 Photos: In pictures: President Trump in Europe The Trumps walk toward Marine One after arriving at London's Stansted Airport on June 3. Hide Caption 42 of 45 Photos: In pictures: President Trump in Europe The President salutes troops as he and the first lady arrive at Stansted Airport. Hide Caption 43 of 45 Photos: In pictures: President Trump in Europe Trump is greeted by UK Foreign Secretary Jeremy Hunt after arriving at the airport. Hide Caption 44 of 45 Photos: In pictures: President Trump in Europe The Trumps arrive at Stansted Airport. 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Less favorable was Trump's view of two left-leaning British politicians. Asked about Labour Party leader Jeremy Corbyn, Trump at first seemed to misunderstand, launching into an attack on London Mayor Sadiq Khan, who Trump deemed "a negative force, not a positive force."

Asked again to respond to Corbyn, who spoke at a demonstration earlier in the day, Trump said he declined a meeting request from the opposition leader.

"He wanted to meet today or tomorrow," Trump said. "I decided I would not do that."

The various opinions on Britain's political life were offered at a difficult moment. May is stepping down as head of her party at the end of the week, entering a lame duck period as the conservatives select a new leader. In some ways, her talks with Trump were purely symbolic since she'll soon hand over her myriad troubles, principally the Brexit matter, to a successor.

But White House and British officials maintained the talks would be substantive, given the general continuity in UK foreign policy between prime ministers and the long list of shared concerns between the two countries.

That includes Iran, which the UK still hopes will adhere to the Obama-era nuclear deal that Trump scrapped, and the Chinese telecom giant Huawei, which the US is working to prevent from establishing 5G networks in Europe and elsewhere.

Trump said during the news conference the two countries would likely strike an agreement on the Huawei issue, and downplayed prospects the US would curb intelligence sharing with Britain as a result.

"We'll be able to work out differences," Trump said. "We have an incredible intelligence relationship."

Cordial affair

Trump and May started the day jointly hosting a breakfast of business chiefs at the Tudor-era St. James's Palace, joined by the President's daughter and senior adviser Ivanka Trump and a dozen or so executives from American and British firms.

At the start of the session, Trump said it had been an "honor" working with his British counterpart and joked she should delay her departure as prime minister until a new trade deal is struck.

"It's an honor to have worked with you," Trump told May. "Stick around. Let's do this deal."

The US President later toured the underground warren of rooms from which Winston Churchill ran his war efforts, a paean to a British leader Trump has long revered and hoped to emulate, at least in photographs.

Instead of taking his armored motorcade from point to point in London this week, Trump has relied on his Marine One helicopter -- even for short distances -- avoiding protests on the city's streets. That included the inflation of a giant balloon depicting Trump as a baby wearing a diaper.

Perhaps because he was traveling over London in the air, Trump claimed on Tuesday to have not witnessed many protests -- and questioned whether they were a fabrication by the media.

"I don't see any protests. I did see a protest today when I came, very small," he said. "A lot of it is fake news."