As the noon deadline for Labour leadership nominations was reached, news filtered through Westminster that the left-wing Jeremy Corbyn had made the ballot. One disconsolate MP remarked: “The party seems to have forgotten every one of Tony Blair’s lessons.” For the former prime minister, the left was an enemy to be fought, not a relative to be indulged. He would never have countenanced the inclusion of Corbyn in the interests of widening debate. Blair wanted the left to be rendered irrelevant. In his memoir, A Journey, he excoriated the “recalcitrant union leaders, bolshie MPs, lefty activists and assorted intellectuals whose main contribution was to explain why nothing should change in the name of being real radicals”.

Corbyn’s presence on the ballot, making him the most left-wing candidate in a Labour leadership contest since Tony Benn fought Neil Kinnock in 1988, has united the Blairites and the old right in revulsion. They believe that the inclusion of the anti-austerity, anti-Trident MP will distort the debate and distract from the question of which contender is the most electable. “This isn’t student politics that we’re playing here. This is about people’s lives,” the backbencher Simon Danczuk told me. One senior Labour MP said that the party had behaved at its “eccentric and naive worst” – “Having my nan on the ballot would widen the debate.”

When Diane Abbott crossed the nominations threshold in 2010 with the aid of David Miliband (which he later regretted), it was partly to avoid an all-male, all-pale leadership election. Few believe that there is any comparable justification for including Corbyn. “If we don’t take ourselves seriously, no one else will,” the shadow energy minister Jonathan Reynolds, a Liz Kendall supporter, lamented. “There is obviously no way Jeremy can win a general election and we have let down all those people who desperately need Labour to be an electable alternative to the Tories.” Others simply complain of how their inboxes and Twitter feeds were wrecked by the unending messages imploring them to nominate Corbyn.

After the need to broaden debate, it was the need to preserve party unity that was most commonly cited as a justification. But an increasing number contend that Labour has long chosen unity over clarity. Ed Miliband, they note, led a superficially harmonious party for five years to little avail. The “Labour family” was kept together but few outsiders chose to join it. The Blairish Kendall declared at the Parliamentary Labour Party hustings that MPs should “debate, decide and then unite”. Unity should follow the result, rather than precede it. Kendall has embraced the “tough love” model of leadership that Miliband explicitly rejected.

MPs concede that “no one really knows” what the impact of Corbyn’s candidacy will be. Some believe that he will prove an arithmetical irrelevance, recalling that Abbott won just 7.42 per cent of the vote in 2010. But if that election had been conducted under Labour’s new “one member, one vote” system, the Hackney North MP would have finished third with 10.4 per cent. Abbott was never forgiven by some on the left for sending her son to private school. Corbyn is so devoted to comprehensive education that his ex-wife claims that their separation was partly down to her decision to send their son to grammar school.

Should a large number of supporters register in order to vote for Corbyn, it is Andy Burnham and Yvette Cooper who will benefit from their second preference votes. To regain her early momentum, Kendall will need to surpass all others in the televised hustings. Her opponents – and some of her supporters – believe that she has already strayed too far from the party’s ideological centre of gravity by loudly endorsing free schools and the use of the private sector in the NHS. Blairites curse Labour’s drift to the left (just two MPs elected for the first time in 2015 nominated Kendall, compared to 12 who nominated Corbyn) but they cannot absolve themselves, or their helmsman, of blame. It was Blair’s adventurism in Iraq and his post-prime-ministerial “dash for cash” that contaminated his political brand. Had he been less dismissive of inequality while in office, others would have been less dismissive of him.

Having derided Gordon Brown and Ed Miliband long before others did, Labour’s right must ask itself why it failed to stop either winning the leadership. The Blairites never settled on a credible challenger to Brown and botched opportunities to remove him. David Miliband’s savage criticisms of his brother’s leadership only magnified his failure to defeat him in 2010. On the night of the general election, the former foreign secretary phoned victorious Labour candidates to congratulate them. Had he shown similar attentiveness towards the 2010 intake (who recall his haughty imperiousness at a post-election gathering), he would have won the prize he still seems to crave. It is ironic that the Blairites, supposedly masters of the political dark arts, have been so repeatedly outplayed by their opponents.

The public insistence that Labour is electing a potential prime minister competes with the private acknowledgment that the next leader is unlikely to rise that far. In my interview with her, Kate Hoey recounts a senior figure telling her: “Oh, don’t be so stupid, Kate. We’re not electing a prime minister. We’re electing a leader of the opposition for ten years.”

In these circumstances, Labour feels polarised between those who aspire to elect a “winner” (or the closest thing available) and those more concerned with salving the wounds inflicted by the electorate. For Blair, who never ceased to remind his party that victory was always preferable to defeat, that is ultimate proof of the failure of his project to outlast him.