Winston Churchill’s ghost still hovers over Washington and London. American presidents have often modeled themselves after the British wartime leader, especially in times of conflict.

George W. Bush was a great admirer. And so in the buildup to the Iraq war, Prime Minister Tony Blair lent him a bust of Churchill, while another one, which had been in the White House for several decades, was being repaired. When President Barack Obama returned the bust after the old one was fixed — as had been agreed before Mr. Obama came to the White House — he was accused by a British politician of doing so out of spite, because of his “ancestral dislike of the British Empire, of which Churchill had been such a fervent defender.”

That politician was Boris Johnson, who became prime minister of Britain on Wednesday. He once wrote a fawning biography of Churchill and did nothing to discourage the impression that he identified with the great man: the upper-class mannerisms, the jokes, the love of grandeur and the appeal, post-Brexit, to the myth of wartime Britain standing alone against the Nazi menace, the much-vaunted “Dunkirk spirit.”

President Trump, who placed a Churchill bust in the Oval Officewith great fanfare, has no upper-class mannerisms or, indeed, manners at all. But he, too, is an admirer of Churchill, and of Mr. Johnson, whom he called, somewhat oddly, the “Britain Trump.” Some supporters of Mr. Johnson see this as a sign that the special Anglo-American relationship will revive in all its old glory. If so, this relationship will stand for everything Churchill — and especially his great wartime ally Franklin D. Roosevelt — despised.

Churchill was indeed a defender of empire and held some serious racial prejudices, especially against Indians, whom he detested. But he was also an internationalist. Far from wanting Britain to go it alone during the evacuation of Allied troops from Dunkirk in the spring of 1940, he even entertained the idea that Britain and France should merge as one nation to fight Hitler.

The idea of Britain’s special relationship with the United States was also very much Churchill’s. His mother was American, so there were sentimental reasons. And Churchill was a great believer in the greatness of the “English-speaking peoples.” But the relationship was born out of dire necessity. Churchill knew that Britain would not be able to defeat Nazi Germany without active help from the United States.

Roosevelt, who was no friend of British imperialism, was well aware of the danger posed to the United States by a Europe dominated by the Third Reich. But in 1940, most Americans were not at all keen to go to war to help Britain. The most fervent opposition came from right-wing isolationists, and some of them, such as the aviator Charles Lindbergh, had more than a sneaking sympathy for the Nazis. Their slogan, revived by the Trump campaign in 2016, was “America First.”

At the end of 1941, the Japanese attack on Pearl Harbor and Hitler’s declaration of war against the United States silenced the America Firsters. Churchill and Roosevelt drew up the Atlantic Charter, envisioning the world after Hitler’s defeat. It was marked by deeply internationalist ideas: cooperation between countries, free trade and political freedom for all. The United Nations, now much disdained by the Trump administration, was born from this charter.