Mr. Corbyn wants to reverse many of these positions. He vehemently opposes foreign military intervention and says he wants to rein in income inequality. He has even said he would renationalize industries. He also wants to give party members power to help shape policy, and to elect his top team.

For most rank-and-file members, the no-confidence vote was not just a vote against Mr. Corbyn, but against this ideological sea change, an impression reinforced by the presence of Mr. Blair’s allies at the forefront of the attempts to unseat Mr. Corbyn. During the leadership campaign in 2015, Mr. Blair himself excoriated Mr. Corbyn and his supporters. In July 2015, he told Labour members that voting for Mr. Corbyn could lead to “annihilation” and said, “If your heart’s with Jeremy Corbyn, get a transplant.”

Thus, many Labour members have viewed challenges to the Corbyn leadership not as about competence, but as about ensuring the left does not gain a significant foothold in the party.

Many of Mr. Corbyn’s opponents are tearing their hair out because his supporters are sticking by him even though everyone seems to believe he is unelectable. But the concept of “electability” is fraught within the party. Members of Parliament and commentators hostile to Mr. Corbyn argue that winning elections should be the Labour Party’s primary goal. And to win elections, they say, the party must support policies that the party’s base opposes, like cutting welfare.

But the issue is not that the Labour base would rather lose elections and remain left-wing; it’s that capitulating to British voters’ more right-wing inclinations does not seem to have worked for the party. In the 2015 general election, Labour’s candidate for prime minister was Ed Miliband, a social democrat who promised “controls on immigration,” and to establish stricter welfare policies. He still lost.

So even when Labour had a moderate, allegedly electable candidate, Britain still ended up with a Conservative government. Rank-and-file members therefore started to see the electability question as a cover for moving the party to the right. Mr. Blair embodied their worst fears when, in a 2015 speech on Labour’s future, he said: “I wouldn’t want to win on an old-fashioned leftist platform. Even if I thought it was the route to victory, I wouldn’t take it.”

The Labour Party has always been an uneasy coalition, and its internal factions are much more varied than simply Blairites and Corbynites. But the attempts to get rid of Mr. Corbyn have pushed Labour’s biggest ideological clash to center stage: on one side, proponents of a professionalized, media-friendly party whose role is to win elections so it can make modest social reforms; on the other, supporters of a social movement that aims to change society starting with the grass roots — but for whom winning parliamentary power is not a goal to be pursued at any cost.

Since New Labour’s first election victory in 1997, the British left has found itself virtually excommunicated from politics. These people are not stupid or crazy. In Mr. Corbyn, they have identified an opportunity to reinsert themselves into public life and to return the Labour Party to its socialist values. They recognize this may be the only chance they have. It’s entirely reasonable that they are taking it.