Blairites only have themselves to blame for their humiliation at the hands of Jeremy Corbyn

The most significant statistic in Labour’s leadership election was not Jeremy Corbyn’s 59.5 per cent share of the vote but Liz Kendall’s derisory 4.5 per cent. It marks the final nail in the coffin of Blairism. The Labour critics of Tony Blair, who have been trying to bury him for years, have succeeded.

Ed Miliband won the leadership five years ago by positioning himself as “not Blair”. But, in the eyes of the left, he was a disciple of Gordon Brown and, despite sound instincts as the son of his Marxist father, allowed Ed Balls too much influence. The last-minute attempt to look tough on the deficit in Labour’s manifesto this May made the party “Tory-lite”, according to the left. It handed Corbyn a perfect platform as an authentic anti-austerity candidate.

Most senior Labour figures – including Miliband, when he resigned the day after the party’s shattering defeat – assumed Labour would turn right and reach for the old Blairite tunes. Surely that was the only route after defeat on a left-of-centre programme. Miliband envisaged a role as a backbench “keeper of the party’s conscience” after the Blairites reassumed control. What no one saw coming was an alliance between Old Labour and Young Labour, enthused by Corbyn and too young to remember the party’s wilderness years in the 1980s.

Kendall was brave but at times her inexperience showed. Saturday’s result tells us that whoever carried the “Blairite” millstone was going to be crushed. When I asked Kendall during the campaign why she was not doing well, she replied with one word: “Iraq”.

The Blairites have tried to reinvent themselves but failed. The Progress group of modernisers dropped the “New Labour” label but no one was fooled. “Please don’t call me a Blairite,” several of the former leader’s allies have pleaded with me in recent years.

The Blairites have only themselves to blame. The seeds of Corbyn’s victory do not lie only in the disastrous Iraq War. Tony Blair lost interest in reforming the party once he got into power. He let trade union dogs lie. Now they are barking again, a force for the left rather than playing their traditional role supporting a moderate leader from the right.

Blair’s rivalry with his one-time partner Gordon Brown fatally damaged the New Labour project. Blair came to believe that Brown was not the right man to succeed him but his chosen heirs were steamrollered by the ruthless Brown machine.

The Blair-Brown split allowed the project to run out of steam. In a revealing admission last month, Lord Mandelson, the “third man”, said a faultline “divided New Labour between Blairites, who espoused greater public service reform, and Brownites, who were more focused on the economy, although personalities played as big a part as policy. It prevented Gordon Brown from taking forward the New Labour reform agenda.”

Miliband compounded the problem by rarely defending Labour’s 13 years in power. Blairite members drifted away. Miliband did not win a majority among Labour MPs in 2010 but 78 made him their first preference (against 105 who chose his brother). Corbyn won the votes of just 20 of Labour’s 232 MPs.

This is why, despite his undoubted mandate among members and his pleas for loyalty, it will prove impossible for the new leader to unite the party.

Labour has long been two parties underneath – a social democratic one and a socialist one. Now it has a socialist leader and party membership who are out of sync with many of its mainly centrist MPs. That doesn’t mean that 200 MPs will be plotting to remove Corbyn from today, since about half of them have close union ties.

It does mean, however, that Labour’s two parties will be on display on a daily basis in Parliament. The Conservatives will not need to set traps to flush out Labour’s splits; the Opposition will advertise its differences.

David Cameron will probably be able to rely on a sizeable number of centrist Labour MPs on a whole range of issues, helping him to compensate for his slender majority of 12. Air strikes against Isis in Syria will be an early test. There will be Commons votes on a third runway at Heathrow; the HS2 rail project and renewing the Trident nuclear weapons system – all opposed by Corbyn. He is also out of step with most Labour MPs on EU and Nato membership and an EU referendum is coming soon.

These divisions will make Labour look shambolic. It may not matter to the 251,000 Labour people who voted for Corbyn, who will see it as part of his new politics. But the rest of the 46 million voters may take a different view. The old maxim that “divided parties lose votes” is going to be tested daily.

To fight back, a new generation of moderates will need to produce forward-looking policies rather than replay New Labour’s greatest hits.

Corbyn’s stunning victory has given Labour its overdue reckoning with the Blair years. The firebreak should allow Labour to stop defining itself against Blair, from whom a period of silence would be welcome. The centrists will need to use what they hope will be a Corbyn interregnum to find a credible leader. Many Labour MPs are convinced he will not lead them into the 2020 election. But the scale of Corbyn’s victory means it will be harder and take longer to dislodge him.

The moderates will not walk away and create a new party. A more likely split scenario is Corbyn being forced out, MPs ensuring no left-winger stands in the ensuing leadership election and the left and the unions breaking away to form a socialist party. The social democrats would be back in control of their party. But, they wonder with good reason, what state would it be in by then?