No question in British politics will be more regularly asked, and reliably brushed aside, over the next few months than when Prime Minister Rishi Sunak plans to call the country’s next general election.

He must do so by January 2025. The conventional wisdom is that with his Conservative Party trailing the opposition Labour Party by 20 percentage points in the polls, Mr. Sunak will wait as long as he can. Given the fact that Britons do not like electioneering around Christmas or in the dead of winter, that would suggest a vote next fall.

But some of Mr. Sunak’s colleagues last week pushed for an earlier timetable. Having lost a critical legal ruling on his flagship immigration policy, the prime minister came under pressure from the right of his party to go to the polls in the spring if the House of Lords blocks the government’s efforts to revamp legislation to deport asylum seekers to Rwanda.

Turning the election into a referendum on immigration might deflect attention from the economic woes plaguing Britain. But that assumes voters could be persuaded to swing to the Conservatives out of a fear of asylum seekers crossing the English Channel in small boats, rather than blaming the party for a stagnant economy, a cost-of-living crisis and hollowed out public services.

Britain’s Supreme Court last week struck down the policy of deporting asylum seekers to Rwanda as unlawful. But Mr. Sunak has vowed to keep the matter alive by negotiating a new treaty with the East African country that would include a legally binding commitment not to remove migrants sent there by Britain — one of the court’s objections.

Mr. Sunak also pledged emergency legislation that would declare Rwanda a safe country for asylum seekers. It remains unclear whether that would survive legal challenges and in the House of Lords, the unelected upper chamber of Parliament that has the right to review the legislation and could block it (though its appetite for a full-scale clash with the government was not clear.)

“I know the British people will want this new law to pass so we can get flights off to Rwanda,” Mr. Sunak told reporters last week. “Whether it’s the House of Lords or the Labour Party standing in our way, I will take them on because I want to get this thing done and I want to stop the boats.”

Political analysts say immigration remains a resonant issue in England’s north and Midlands, where support for the Conservatives in 2019 gave the party a landslide general election victory. Those voters, many of whom traditionally supported the Labour Party, were drawn to the Tory slogan, “Get Brexit done.”

“Immigration is now the top priority for 2019 Conservative Party voters, above even the cost-of-living crisis and the dire state of the country’s National Health Service,” said Matthew Goodwin, a professor of politics at the University of Kent, who has written about populism and identity politics.

“This means, in short, that Rishi Sunak has no way of winning the next election unless he connects with these voters by reducing immigration and regaining control of the country’s borders,” he said. “Yet both of those things currently look unlikely.”

Far from accelerating the date of an election, Professor Goodwin argued that the salience of immigration would pressure Mr. Sunak to delay a vote. It will take months to surmount the legal problems with the existing policy, the professor said, let alone begin one-way flights to Rwanda.

Other experts are more skeptical that an immigration-dominated election would play to the advantage of the Tories. Most voters view the party negatively on immigration, said Sophie Stowers, a researcher at the U.K. in a Changing Europe, a think tank in London. The number of people crossing the channel has remained stubbornly high since Mr. Sunak became prime minister, while legal migration has soared.

“To me, it seems counterintuitive to bring attention to an issue where you have a poor image with the public,” Ms. Stowers said.

The question is whether the Conservatives would do even worse if the election were decided on the economy, which matters more than migration to voters at large, according to opinion polls. Mr. Sunak did achieve one of his key economic goals last week, halving the rate of inflation. But he has yet to achieve the other two: reviving growth and reducing public debt.

It’s not yet clear that the economic news will improve between the spring and fall, analysts said. While inflation has cooled, the lingering effect of higher interest rates — propelled upward by Liz Truss’s market-shaking tax policies last year — is still cascading through the economy in the form of higher home mortgage rates.

Historically, many successful prime ministers, including Margaret Thatcher and Tony Blair, called elections earlier than they needed, rather than risk becoming the victim of unforeseen events. They usually opted for the summer months, when the weather — and the public mood — is typically better, although Boris Johnson successfully broke that pattern with his victory in December 2019.

Mr. Sunak’s room for maneuver is limited. One option would be holding the vote in May 2024 to coincide with local elections, or in June. Another possibility would be October or November, which would coincide with elections in the United States. But the possibility of a victory by Donald J. Trump could have an unpredictable effect, potentially pushing some British voters to a more centrist option. As a last resort, Mr. Sunak could hold off until Jan. 28, 2025.

Some of Mr. Sunak’s predecessors paid a high price for miscalculating the timing of elections. Despite speculation that he would call an election in 1978, the Labour Party prime minister James Callaghan delayed voting until the following year. Labor unrest escalated into what became known as the “winter of discontent,” sweeping Mrs. Thatcher to victory in 1979.

Gordon Brown, another Labour prime minister, had been expected to capitalize on his early popularity by calling an election soon after taking over from Tony Blair in 2007. Instead, he delayed, ultimately losing power in 2010.

Theresa May made the opposite decision, calling an early election in 2017 in which she lost her majority, though probably more because of her unpopular agenda and poor campaign skills than bad timing.

“Once the election is underway, everything is on the table,” said Peter Kellner, a polling expert. “You lose control of the agenda.”

Trying to build an election campaign around the issue of small boats bringing migrants is likely to fail, Mr. Kellner added, suggesting Mr. Sunak will only call an early vote if he calculates he has a realistic prospect of keeping his job.

“If, at the point when you have to make a decision, you have no chance of winning, then you might as well wait,” he said, “because maybe there is a five percent chance of winning in six months, and a five percent chance is better than no chance.”