LONDON When President Trump called the pro-Brexit politician Nigel Farage to the stage during his rally in Goodyear, Ariz., on Wednesday, it was a reminder that Britains bombshell vote to leave the European Union in June 2016 was seen as a harbinger of Mr. Trumps victory in the United States that fall.

And yet, four years later, Mr. Farages appearance seemed less a powerful display of populist camaraderie than a strange throwback. Britain has moved on from Brexit and Mr. Farage is viewed as yesterdays man, forced to travel abroad to seek a spotlight that has swung away from him at home.

Britain seems equally ready to turn the page on Mr. Trump. Despite his staunch support of Brexit and his effusive displays of affection for Prime Minister Boris Johnson, Mr. Trumps potential defeat next week is viewed by most Britons with equanimity, if not enthusiasm, given his unpopularity across the political spectrum.

There are millions and millions of Brits who voted for Brexit and think Donald Trump is ghastly and something quite different, said Timothy Garton Ash, a professor of European studies at Oxford University.

Even for those elite Brexiteers who had a vision of Britain and the U.S. creating an Anglosphere as an alternative to the E.U., its fairly clear that Donald Trump doesnt share that vision, he said.

Inside Mr. Johnsons government, where a Trump defeat has been a source of anxiety for months, officials now talk about how they could adjust to a President Joe Biden and perhaps even take advantage of a change in the White House. On their No. 1 priority an Anglo-American trade deal they say they could Bidenize whatever they have negotiated with Mr. Trump to make it palatable to a Democratic administration.

In foreign policy, diplomats spin visions of Britain standing alongside the United States in a coalition of democracies against the commercial and geopolitical pressure of autocrats in China and Russia. That is a role Mr. Johnson could never comfortably play with a president who relishes the company of strongmen.

They foresee Britain working with a Biden administration to tackle the global scourges of the coronavirus pandemic and climate change big-ticket projects that could elevate the Group of 7 summit of world leaders and the United Nations Climate Change Conference, which are to take place in Britain next year.

Its not as if the fundamental relationship is at risk, said Karen Pierce, the British ambassador to the United States. With any new administration, you have to show youre a good partner, and this is true regardless of whether its Democratic or Republican.

There is, to be sure, a healthy dose of rationalization in all this. A Biden administration would present Britain with a number of hurdles, starting with trade. Mr. Trump promised Mr. Johnson a lucrative deal, which the prime minister made a selling point in his own election campaign promising to Get Brexit done. But Mr. Biden has other priorities overseas and may not view a conventional free-trade agreement with Britain as much of a prize.

The British, some American experts said, were deluding themselves if they thought they could satisfy Mr. Biden by tacking on a couple of provisions on labor and environmental standards to their half-finished deal with Mr. Trump.

Its a little tone-deaf to say, We have this deal with Trump. What icing do you want on the cake to make it a Biden deal? said Thomas Wright, the director of the Center on the United States and Europe at the Brookings Institution in Washington.

Biden is going to want to demonstrate to the middle class that there is a different way of doing foreign economic policy, he said. I dont know if starting out with a traditional trade agreement is something theyre going to want to do.

The problem is, Britain cannot afford the luxury of starting negotiations from scratch. Trade Promotion Authority, the American measure that puts trade agreements on a fast track through Congress, will expire in July. In order to ensure a deal with Britain stayed on that fast track, the White House would need to notify Congress about it by next April.

Mr. Johnson risks stumbling into another difficult area with Mr. Biden over Ireland. His governments recent move to rewrite parts of its Withdrawal Agreement with the European Union that deal with Northern Ireland is viewed by Democrats in Washington as a threat to the Good Friday Agreement, a deal brokered by President Bill Clinton that settled decades of sectarian strife.

Mr. Biden has posted a tweet warning Mr. Johnson that any trade deal between the U.S. and U.K. must be contingent upon respect for the Agreement and preventing the return of a hard border. Period.

Nov. 2, 2020, 7:03 p.m. ET

British officials said they recognized the sensitivity of Ireland for Mr. Biden, who speaks fondly of his Irish roots. But those complications, analysts say, pale beside the thorny issues that could arise in a second Trump term when, for example, the president could decide to pull the United States out of the NATO alliance.

At Mr. Trumps rally, Mr. Farage framed the American election as a referendum on the forces that drove Brexit, as well as Mr. Trumps first victory. He recalled coming to the United States in 2016 to bring the Brexit message that you can beat the establishment, and that is what Donald Trump did.

Mr. Johnsons government has clung to some of that anti-establishment fervor. But the bitter debates that cleaved British society for three-and-a-half years after the referendum have subsided in part because of sheer exhaustion and in part because they have been eclipsed by worries about the pandemic.

Whatever the parallels between Brexit and Mr. Trump, the president has never enjoyed the affection of the British public. In a recent poll of European attitudes toward the election, the British favored Mr. Biden over Mr. Trump by a margin of 61 percent to 13 percent, according to the research group YouGov.

If Britain were to rerun the 2016 referendum today, Mr. Garton Ash said, polls suggested that Brexit would probably lose, too, if not by as thumping a margin as Mr. Trump might among Britons. But the vast majority of voters have no interest in revisiting the issue, which is why Mr. Farage has been left without a cause in a country where he once loomed large.

Exhausted by politics and besieged by the coronavirus, British voters seem attracted to some of the same qualities in Mr. Biden that American voters are.

There are lots of intelligent, skeptical voters in Britain who like the idea of Joe Biden, Mr. Garton Ash said. Most of them see their vote for Brexit as distinct and different from Trump.

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