When Prime Minister Rishi Sunak said this week that he was not likely to call a general election in Britain before the second half of the year, he was trying to douse fevered speculation that he might go to the voters as early as May. But in doing so, he set up another tantalizing prospect: that Britain and the United States could hold elections within days or weeks of each other this fall.

The last time that happened was in 1964, when Britain’s Labour Party ousted the long-governing Conservatives in October, and less than a month later, a Democratic president, Lyndon B. Johnson, swept aside a challenge from a right-wing Republican insurgent. The parallels to today are not lost on the excitable denizens of Britain’s political class.

“It’s the stuff of gossip around London dinner tables already,” said Kim Darroch, a former British ambassador to Washington who is now a member of the House of Lords. For all the Côte du Rhône-fueled analysis, Mr. Darroch conceded, “it’s hard to reach any kind of conclusion about what it means.”

That doesn’t mean political soothsayers, amateur and professional, aren’t giving it a go. Some argue that a victory by the Republican front-runner, Donald J. Trump, over President Biden — or even the prospect of one — would be so alarming that it would scare voters in Britain into sticking with Mr. Sunak’s Conservative Party, as a bid for predictability and continuity in an uncertain world.

Others argue that the Labour Party leader, Keir Starmer, could win over voters by reminding them of the ideological kinship between the Conservatives and Mr. Trump, who remains deeply unpopular in Britain. Mr. Trump praised Mr. Sunak last fall for saying he wanted to water down some of Britain’s ambitious climate goals. “I always knew Sunak was smart,” Mr. Trump posted on his Truth Social account.

Still others pooh-pooh the suggestion that British voters would make decisions at the ballot box based on the political direction of another country, even one as close and influential as the United States. Britain’s election, analysts say, is likely to be decided by domestic concerns like the cost-of-living crisis, home-mortgage rates, immigration and the dilapidated state of the National Health Service.

And yet, even the skeptics of any direct effect acknowledge that near-simultaneous elections could cause ripples on both sides of the pond, given how Britain and the United States often seem to operate under the same political weather system. Britain’s vote to leave the European Union in June 2016 is often viewed as a canary in the coal mine for Mr. Trump’s victory the following November.

Already, the campaigns in both countries are beginning to echo each other, with fiery debates about immigration; the integrity — or otherwise — of political leaders; and social and cultural quarrels, from racial justice to the rights of transgender people. Those themes will be amplified as they reverberate across the ocean, with the American election forming a supersized backdrop to the British campaign.

“The U.S. election will receive a huge amount of attention in the run-up to the U.K. election,” said Ben Ansell, a professor of comparative democratic institutions at Oxford University. “If the Tories run a culture-war campaign, and people are being fed a diet of wall-to-wall populism because of Trump, that could backfire on them.”

Professor Ansell identified another risk in the political synchronicity: it could magnify the damage of a disinformation campaign waged by a hostile foreign power, such as the efforts by Russian agents in Britain before the Brexit vote, and in the United States before the 2016 presidential election. “It’s a two-for-one,” he said, noting that both countries remain divided and vulnerable to such manipulation.

On Thursday, Mr. Starmer appealed to Britons to move past the fury and divisiveness of the Brexit debates, promising “a politics that treads a little lighter on all of our lives.” That was reminiscent of Mr. Biden’s call in his 2021 inaugural address to “join forces, stop the shouting, and lower the temperature.”

Frank Luntz, a Republican strategist who studied at Oxford and has advised Conservative Party officials, said he warned the Tories not to turn their campaign into a culture war. “It will get you votes, but it will destroy the electorate in the process,” he said he told them, pointing out that a campaign against “woke” issues had not helped Gov. Ron DeSantis of Florida dislodge Mr. Trump.

Mr. Sunak has vacillated in recent months between a hard-edge and more centrist approach as his party has struggled to get traction with voters. It currently lags Labour by 20 percentage points in most polls. While general elections are frequently held in the spring, Mr. Sunak appears to be playing for time in the hope that his fortunes will improve. That has drawn criticism from Mr. Starmer, who accused him of “squatting” in 10 Downing Street.

“I’ve got lots that I want to get on with,” Mr. Sunak told reporters Thursday. He could wait until next January to hold a vote, though analysts say that was unlikely, since campaigning over the Christmas holiday would likely alienate voters and discourage party activists from canvassing door to door.

With summer out for the same reason, Mr. Sunak’s most likely options are October or November (Americans will vote on Nov. 5). There are arguments for choosing either month, including that party conferences are traditionally held in early October.

In October 1964, the Conservative government, led by Alec Douglas-Home, narrowly lost to Labour, led by Harold Wilson. Like Mr. Douglas-Home, Mr. Sunak is presiding over a party in power for more than 13 years. The following month, President Johnson trounced Barry Goldwater, the hard-right Republican senator from Arizona, who had declared, “Extremism in the defense of liberty is no vice.”

Sixty years ago, the Atlantic was a greater divide than it is today, and the links between trans-Atlantic elections more tenuous than they are now. Mr. Trump, armed with a social media account and a penchant for lines even more provocative than Mr. Goldwater’s, could easily roil the British campaign, analysts said.

And a Trump victory, they added, would pose a devilish challenge to either future British leader. While Mr. Trump treated Mr. Sunak’s predecessor, Boris Johnson, as an ideological twin, he fell out bitterly with Mr. Johnson’s predecessor, Theresa May, and there was little reason, they said, to hope for less drama in a second Trump term.

The biggest pre-election danger — much more likely for Mr. Sunak than for Mr. Starmer, given their politics — is that Mr. Trump will make a formal endorsement, either while he is the Republican nominee or newly elected as president, said Timothy Bale, a professor of politics at Queen Mary, University of London.

“Given how negatively most Brits feel toward Trump,” Professor Bale said, “such an endorsement is unlikely to play well for whichever of the two is unlucky enough to find favor with him.”

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