LONDON — IF you think Donald J. Trump’s early lead in the race for the Republican presidential nomination is the season’s most spectacular case of unlikely political ascendancy, think again. In Britain, a 66-year-old left-wing member of Parliament named Jeremy Corbyn is close to becoming the leader of the Labour Party.

If he prevails, he will most likely be its candidate for prime minister in 2020. The leadership vacancy followed the resignation of Ed Miliband after Labour’s dismal showing in the May election, which enabled David Cameron’s Conservative Party to form a government.

Mr. Corbyn, who has been in the House of Commons since 1983, is an old-fashioned, unapologetic socialist. Compared to Senator Bernie Sanders, he is, in many respects, even more radical. Imagine if a figure like Noam Chomsky or Michael Moore were in Congress and became the front-runner for the Democratic nomination for the White House.

Mild-mannered in person, Mr. Corbyn is demagogic on a podium. Though his party has made accommodations with globalization, consumerism, individualism and the decline of labor as a political force, he has represented a fixed point of anticapitalist ideology for decades.

He opposes austerity cuts and would raise taxes sharply. He idolized the Venezuelan socialist leader Hugo Chávez (who died in 2013), and has described as friends officials from Hezbollah and Hamas, Islamist movements that the United States government considers terrorist organizations. And he believes in unilateral nuclear disarmament for Britain.

Yet, far from being considered the retro candidate in the leadership contest, Mr. Corbyn has emerged as favorite. He is the leading choice of local party branches and is backed by the trade union Unite, which is the party’s most important donor. Opinion surveys suggest that Mr. Corbyn is on course to win against his more moderate or centrist rivals: Andy Burnham, Yvette Cooper and Liz Kendall.

Whatever happens, he will be a force in the movement, a maverick transformed into a party baron.

Mr. Corbyn’s rise has caused some consternation. The former prime minister Tony Blair, who led Labour to three successive election victories by jettisoning precisely what Mr. Corbyn stands for, has warned the party against a regression to left-wing purism. To those who say that their heart tells them to vote for Mr. Corbyn, Mr. Blair said, “Get a transplant.”

Mr. Blair’s analysis is hard to refute, but so far the party is deaf to his entreaties. Ms. Kendall, the only candidate who shares Mr. Blair’s perspective, is running fourth. Ms. Cooper and Mr. Burnham are both capable politicians, but neither communicates a sense of urgency or passion.

To win the 2020 election, which will follow redistricting, the Labour Party would need an additional 106 seats in the House of Commons. To achieve this, it must woo Conservative voters.

In Scotland, the dynamic is different. Labour must try to take seats from the left-wing Scottish Nationalist Party. But at present, there are only 59 constituencies in Scotland, so a Labour strategy based on competing with the S.N.P. will fail if applied across the rest of Britain.

This points to the heart of the problem. With the exception of Ms. Kendall, none of the candidates would follow a Blairite template for winning back moderate Conservatives. Although Mr. Miliband, who earned the nickname “Red Ed,” already tested to destruction the theory that Britons had shifted leftward, the left is overweening, contemptuous of the “Blairite comfort blanket” — the idea that tacking back toward the center would make Labour more electable.

In practice, there’s nothing comforting in Mr. Blair’s message. He’s asking a progressive party to confront the bleak reality that millions of decent people are fearful that voting Labour in 2020 would be an act of self-harm.

When I hear Mr. Corbyn speak — and he speaks very well — I recall a story from Mr. Blair’s great ally Peter Mandelson. He recalled being told by a far-left colleague during Labour’s long years of opposition, from 1979 to 1997, that there must be “no compromise with the electorate.”

Why won’t the party compromise?

After 1989, the British left no longer felt contaminated by Soviet totalitarianism. And since the 2008 financial crash, the old-fashioned socialists within Labour have mistaken public anger against banks as evidence that the hour of anticapitalist true believers had come. Critics have also used Mr. Blair’s errors over intervening in Iraq to besmirch his overall achievement. So it is the left that has found an unwarranted confidence this summer.

The party’s registered voters have until Sept. 10 to avoid a fatal error. It is Mr. Corbyn who offers a comfort blanket, inviting his supporters to wrap themselves in the illusory warmth of ideological nostalgia that will, in reality, consign Labour to chilly irrelevance.