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.”