During a formal dinner at Buckingham Palace, Queen Elizabeth II offered a toast to Trump, and Trump responded in kind.
"I doubt very seriously Donald Trump is the favorite of the queen, but she spoke as she did about him and welcomed him for the same reason he spoke about her in the way he did," Hume claimed.
"The relationship is bigger than any of this stuff between the politicians," he added, pointing to Trump and London Mayor Sadiq Khan trading barbs in advance of the visit.
"You can see [it] in the actions of the mayor of London, whose popularity is down in a city which isn't particularly fond of Trump. So, he takes Trump on and of course, Trump bites."
Trump later tweeted that Khan reminded him of New York City Mayor Bill de Blasio - with whom he also has sparred - and labeled the London mayor a "stone cold loser."
Hume said the political differences between Trump and some of the dignitaries in Great Britain were separate from the bond America has had with the U.K.
"These state visits involving these two countries really aren't about the personalities that are presiding at the time."
"Politicians do what politicians do. This relationship goes on," he said, adding the two nations have stuck together through "dark days" and in advance of victory in World War II.
Fox News' Bret Baier and Edmund DeMarche contributed to this report.