Clement Attlee, Margaret Thatcher, Jeremy Corbyn. The first two led transformative governments that established a new political settlement in Britain: and make no mistake, the Corbyn project’s aspirations are no less ambitious. Attlee sought to overturn a failed system that delivered the great depression, the hungry 1930s and a genocidal world war. The Tories resigned themselves to the underlying assumptions of Attleeism, much to Thatcher’s chagrin. British politics became a “socialist ratchet”, she claimed, while the Tories merely “loosened the corset of socialism; they never removed it”. Thatcher strove to use a crisis spurred on by a global oil shock to smash Attlee’s consensus: this time, it was Labour’s time to surrender, with Tony Blair described by Thatcher herself as her “greatest achievement”.

Labour conference 2017: Jeremy Corbyn's keynote speech – as it happened Read more

Both Attleeism and Thatcherism had iconic moments that came to represent the bankruptcy – as they saw it – of the system they replaced. Postwar social democracy had the Jarrow hunger marches of the 1930s. Thatcherism had the winter of discontent. For Britain’s ascendant new left, it is the horror of Grenfell Tower: dozens of working-class people killed in a society that prioritises profit not just over people’s needs and aspirations, but even their lives.

“It stands for a failed and broken system,” Corbyn declared to rapturous applause, “which Labour must and will replace.” Labour had a “new model of economic management”, and it would “replace the failed dogmas of neoliberalism”. Labour’s mission was not simply reversing austerity, “but to transform our economy with a new and dynamic role for the public sector”. Democracy would be brought to the economy and the workplace, in an attempt to realise “a fundamental and irreversible shift in the balance of power and wealth in favour of working people and their families”, as Labour’s 1974 manifesto put it.

Play Video 4:19 Jeremy Corbyn's conference speech in four minutes – video highlights

The political wisdom of our time has been this: unless you accept lower taxes on the rich, an ever-expanding role for the private sector, deregulation, a limited role for government, weakened trade unions, and so forth, you are rendered unelectable. This was called the “centre ground”. But, as Corbyn noted, the “political centre of gravity isn’t fixed or unmovable”. Attlee audaciously ripped up the political mantras of his era – usurping power from a wartime hero no less. In the 1945 general election campaign, Winston Churchill even hysterically argued Labour would “fall back on some sort of Gestapo” to implement its policies.

Thatcher, too, rebelled against a consensus whereby Tories fought elections “largely on policies which 20 years ago were associated with the left, repudiated by the right”, as Labour’s Tony Crosland hubristically declared in the 1950s. Both Attlee and Thatcher had to confront those in their own party who were wedded to the certainties of the old system. Attlee expelled Labour MP Alfred Edwards for rebelling against the nationalisation of steel, while Ivor Bulmer-Thomas jumped before he was pushed; Thatcher had to confront the Tory “wets” who believed a break with Keynesianism was neither politically possible nor even desirable. The parallels with Corbyn’s Labour hardly need stating.

Play Video 7:59 Owen Jones at the Labour conference: 'There's been a peaceful revolution under Corbyn' - video

The calamity of the great depression and the second world war ushered in Attleeism; rampant stagflation was the midwife of Thatcherism. At the time of the 2008 financial crash there was a widespread misplaced schadenfreude on the left. Surely market fundamentalism had been discredited; surely the west’s ruling economic elites – and their political representatives – would be held to account; surely the left would rise from the ashes. Instead came a tidal wave of austerity, devastating attacks on the remaining social gains of social democracy, and the poison of rightwing xenophobia.

Migrants and benefit claimants became the scapegoats, while the bailed-out banks continued to pay record bonuses as they benefited from further tax cuts. Just two years ago the Tories secured a majority after five years of austerity, defying Bank of England governor Mervyn King’s prediction before the 2010 election that whoever won would be “out of power for a whole generation” because of the severity of the cuts. It was a political nightmare. No wonder, then, there was such applause when Corbyn declared: “2017 may be the year when politics finally caught up with the crash of 2008.”

It is important to understand the political complexion of the Labour conference that so loudly applauded Corbyn’s speech. These are activists who were disillusioned and angered by three things: the Thatcherite juggernaut of the 1980s, the great New Labour compromise with Thatcherism, and the post-2010 austerity offensive. They craved a political alternative, and were ridiculed and demonised and ignored for doing so. Their applause was as much about vindication: they knew that if Labour had offered a timid manifesto, offering only to meekly tinker with the system, then the party would not have secured the biggest increase in its vote share since Attlee himself. To go from political pariahs to the “political mainstream”, as Corbyn put it, was a moment of exhilaration those activists greeted with a standing ovation.

Play Video 7:59 'Jeremy Corbyn has exceeded expectations': Sadiq Khan talks to Katharine Viner – video

In truth, leftwing ideas have long reflected prevailing wisdom in public opinion, whether it be public ownership or higher taxes on the rich. But that popular mood needed to be successfully harnessed. The promise of a “new consensus” emerging from the crash and austerity is now aided by one thing: the Tories are suffering an ideological crisis of confidence. Do they double-down in defence of a system built by Thatcher, which is rapidly losing public consent, or do they start surrendering to the arguments of their opponents?

Labour has not yet won. The Tories are unlikely to run such an inept campaign next time round. The party still needs to win the support of more older voters if it is to secure the significant majority it requires to guarantee sweeping political change. If Labour wins power, the vested economic interests it intends to challenge will fight back.

Attlee and Thatcher worked hard to cement their political legacy, so it proved politically difficult to repeal. Labour must think hard about how it does the same. But as both Attlee and Thatcher captured the spirit of their time, so too has Corbynism. The old order is decaying; its morbid symptoms are everywhere. Socialism is back. And that will be cheered far beyond the applauding activists by the beach in Brighton.

• Owen Jones is a Guardian columnist