Nearly 20 years ago, a wry young human rights lawyer, Keir Starmer, told a documentary filmmaker that it had struck him as “odd” to receive the title of Queen’s Counsel, “since I often used to propose the abolition of the monarchy.”

Mr. Starmer, now the leader of Britain’s Labour Party, has long since disavowed his anti-monarchy statements as youthful indiscretions. In 2014, he knelt before Charles, then the Prince of Wales, who tapped him on the shoulder with a sword and awarded him a knighthood.

If Sir Keir Starmer is swept into 10 Downing Street in the general election next week, as polls suggest he will be, he may end up more politically in sync with Charles then the last two Conservative prime ministers, Rishi Sunak and Liz Truss, whose terms have overlapped with the king’s reign.

On issues including climate change, housing, immigration and Britain’s relations with the European Union, experts say, Mr. Starmer is likely to find common ground with a king who holds longstanding, often fervent, views on those issues but is constitutionally barred from taking any role in politics.

“A Labour government under Keir Starmer will be more attuned to the plight of people as a social issue,” said Ed Owens, a historian who studies the royal family. “These kinds of issues have long been on the radar of the king. There’s a meeting of minds in terms of the social issues at stake.”

If elected prime minister, Mr. Starmer would hold a weekly meeting with Charles, the contents of which would be strictly between them. But people who know Buckingham Palace and Downing Street said they could foresee a fruitful relationship between the 75-year-old monarch and the 61-year-old lawyer, who was knighted for his services to criminal justice as director of public prosecutions.

Beyond Mr. Starmer’s progressive politics, scholars said that Charles would appreciate the stability that a Labour government might restore after the divisions, political upheaval and revolving door of leaders that followed Brexit. In less than two years on the throne, after all, Charles could soon be on his third prime minister.

“The monarchy seeks to be a unifying force, holding the country together, so it favors consensus rather than division,” said Vernon Bogdanor, a professor at Kings College London and an authority on constitutional monarchy. “That is how the king sees his role.”

But Professor Bogdanor added, “While his mother represented the wartime generation, the king is more representative of the ’60s generation.”

As sovereign, Charles does not vote. But in his decades as heir, he was outspoken about issues he cared about, such as organic farming and architecture. Occasionally, his views on more politically charged issues leaked out.

In 2022, Charles was reported to have criticized the Conservative government’s plan to put some asylum seekers on one-way flights to Rwanda as “appalling.” His comments, made in a private meeting, surfaced in The Times of London and The Daily Mail weeks before he represented Queen Elizabeth II at a meeting of Commonwealth countries in Kigali, the Rwandan capital.

Clarence House, where Charles then had his office, declined to comment on the reports, but it did not deny them.

That prompted Boris Johnson, who was then the prime minister and proposed the Rwanda plan, to complain to Charles, according to Mr. Johnson’s communications chief at the time, Guto Harri. In The Mail, he described Mr. Johnson “squaring up to the prince and confronting him about what he — as unelected royalty — had said about the actions of a democratically elected government.”

Charles said nothing about Rwanda after that. In April, after Parliament passed a revised version of the legislation under Mr. Sunak, the king gave it his royal assent, as is his duty, making it law. But Mr. Starmer has vowed that a Labour government would scrap the plan, calling it costly and unworkable.

Climate policy is another area where the king might find a Labour government more aligned with his views. Ms. Truss asked Charles not to attend a U.N. climate change conference in Egypt in 2022, depriving him of a platform to speak out on perhaps his most cherished issue. Mr. Sunak later backtracked on some of Britain’s emission-reduction targets, citing their onerous cost during a cost-of-living crisis.

Labour, by contrast, announced a green investment plan worth 28 billion pounds, or about $35 billion, a year, though it has since suspended the spending targets until Britain’s public finances improve.

“It does sound like a new Labour government and Charles would be in step on these issues,” Mr. Owens, the historian, said. “But Labour has many fine words on the importance of a green agenda. Can they match those fine words with action?”

Mr. Starmer’s devotion to the law might also spare the king the kind of quandary his mother faced in 2019. Mr. Johnson asked her to suspend, or prorogue, Parliament at a time when lawmakers were maneuvering to delay his plan to pull Britain out of the European Union.

The queen assented, but the British Supreme Court later ruled that the decision was unlawful. Critics assailed Mr. Johnson for putting Elizabeth in an untenable position, since she could not defy an elected government. Ms. Truss raised similar questions of governance when she proposed sweeping unfunded tax cuts in 2022, which set off a backlash in the financial markets that sunk her premiership.

“These prime ministers were able to run roughshod over the rules,” Mr. Owens said. “Generally speaking, the monarchy doesn’t like it when too much attention is focused on the Constitution.”

As counterintuitive as it might seem, historians say that Elizabeth had more cordial relations with Labour prime ministers than with Conservative ones. She was viewed as particularly comfortable with Harold Wilson, a down-to-earth Yorkshireman, while her exchanges with Margaret Thatcher, a Conservative icon, were said to be occasionally prickly.

To be sure, the early Labour Party had an anti-monarchy strain. Its first parliamentary leader, Keir Hardie — Mr. Starmer has the same first name — once wrote: “Despotism and monarchy are compatible; democracy and monarchy are an unthinkable connection.”

Conservative political operatives dusted off the video of a young Mr. Starmer and put it in ads suggesting that Labour hated the monarchy. But even before Mr. Starmer took over, Labour had evolved into a reliably constitutional party. And analysts say that residual anti-monarchist feelings were most likely swept away by his purge of the party’s hard left after he became leader in 2020.

At Labour’s party conference in 2022, after the queen’s death, the national anthem was played for the first time. Mr. Starmer, the man who once talked of abolishing the monarchy, raised his voice and sang, “God Save the King.”