Some already say that with his rejection of free-market economics and his quiet but more compromising approach to Britain’s exit from the European Union, he might not just change the Labour Party but also shift British politics more broadly.

“This was about millions inspired by a radical manifesto that promised to transform Britain, to attack injustices and challenge the vested interests holding the country back,” wrote Owen Jones, a columnist for The Guardian. “So, yes — to quote a much-ridiculed Jeremy Corbyn tweet: the real fight starts now.”

Mr. Corbyn is a different type of politician, one happier on the campaign trail speaking to fellow activists through a megaphone than debating in the neo-Gothic splendor of the British Parliament with its arcane rules and obscure traditions.

In 2015, after more than three decades as a lawmaker, he had to be persuaded to stand for the party leadership, agreeing only reluctantly and in order to enable the left to present a candidate. No one, not even Mr. Corbyn himself, expected him to win. If ever there were an accidental leader, he is it.

During his 34 years in Parliament, Mr. Corbyn has essentially been in permanent opposition, not just to Mrs. May’s Conservative Party but also to his own Labour Party. He voted against the Iraq invasion, has opposed successive attempts to roll back civil liberties in the fight against terrorism and has long argued against deregulation and free-market reforms.

The biggest problem, he has said, is that since Margaret Thatcher established neoliberalism as the dominant economic consensus in Britain in the 1980s, Labour allowed the Conservatives to set the agenda on the economy and never offered an alternative narrative.

Mr. Corbyn offered that alternative: Under the banner of “For the Many Not the Few,” he vowed to nationalize the railroads, make universities free again and inject billions into the National Health Service by raising taxes on companies and the top 5 percent of income earners.