With the party on its knees, an implausible leftwing Labour leader with pacifist inclinations is replaced by a strait-laced lawyer from the soft left. A few short years later, Britain is plunged into deadly turmoil, one that exposes hitherto ignored injustices, while an ideologically shapeshifting Tory prime minister with surging popularity expands the state’s role in the economy to an unprecedented degree. But Labour’s radicalism remains undimmed; the party recognises that revolutionary times require revolutionary answers.

The implausible Labour leader was George Lansbury in 1935; his successor was Clement Attlee; and the Tory prime minister who seemed to be the master of all before him was Winston Churchill. As Keir Starmer wins a decisive victory to become the 22nd leader of the Labour party in its 115-year history, a new 1945 seems, for now, a distant prospect. He assumes the leadership in unenviable circumstances. Labour was battered in December’s election; the party has been traumatised by half a decade of internal strife; the Brexit culture war has polarised the nation and wreaked havoc among the party’s electoral coalition; and the UK is being convulsed by its greatest crisis since the guns fell silent three-quarters of a century ago.

But Starmer can succeed, and anyone with progressive sympathies should actively will his leadership to do so. His democratic mandate is rooted in a policy prospectus which, before 2015, would have been deemed unthinkably radical by mainstream Labour: hiking taxes on the rich and big business to fund public investment; democratic public ownership of utilities and services; expanding the welfare state; the abolition of tuition fees; a green industrial revolution; defending migrants’ rights; an end to illegal wars. Starmer declared that Labour’s 2017 manifesto – which punctured a suffocating generation of “there is no alternative”– was the party’s foundational document.

In one of his campaign videos, Starmer rightly declared that Labour must hold Boris Johnson to account for the promises made in his election campaign. The same applies to Starmer; here are red lines that cannot be crossed, the reasons thousands of members who voted for Jeremy Corbyn in two leadership elections have placed their trust in him. What hurt Corbyn, in the end, was not being seen as dangerously extreme. It was instead that Brexit unfairly made him seem like a flip-flopper who would say anything to win power. But there is cause for optimism: Starmer’s allies are emphatic that his commitments are an authentic expression of his own beliefs.

When Corbyn became leader, many of his opponents within the Labour party embraced a scorched earth policy. They desperately wanted him to fail, craving vindication more than displacing a Tory government. They cheered every misstep and failure throwing relentless tasty morsels to insatiable vultures in the rightwing media. They actively destabilised his leadership. Some on the aggrieved left may ask why they should behave any differently. It would achieve nothing except to prolong the Tory nightmare and alienate the wider membership. Now is the time for critical friendship; dissent should be in the context of willing the triumph of a radical Labour government.

There will be those who now want the left to go and find the nearest ditch to die in. So, let’s be clear from the outset: we aren’t going anywhere. Already, those who caricatured Corbynism as an era of authoritarian Stalinism are demanding bloodthirsty purges, to permanently smash the left once and for all. In the coming days and weeks, those elements will do all they can to provoke and demoralise the left. Don’t listen to them: this is your party. Every socialist who rips up their membership card, who retreats from political activity, who finds sanctuary in a dead-end leftwing sect, will be cause for celebration for those hankering for a Blairite revival.

The mistake many “centrist” voices have made is to dismiss political phenomena they do not like – from Corbynism to Brexit to Trump – as simply being mass irrationality, stupidity and hysteria. But Corbyn secured a landslide victory in 2015 because all of the other flanks of the Labour party were politically and intellectually exhausted. Labour’s social democrats had abandoned social democracy; the last consistent social democrats left standing were Labour’s left flank. All of its sister parties were in crisis, including those – like the German Social Democrats – who had stuck to the “third way” playbook. Just two years after what was then one of the party’s worst defeats, and in the aftermath of a vicious civil war, Labour came within 2,227 votes and seven constituencies of forming a government in 2017.

Today’s two major success stories for the European left are the Spanish and Portuguese governments, where social democratic parties have swung leftwards after making pacts with the radical left. It is no coincidence that younger voters in the US, Spain, Portugal and the UK embraced the new left movements at the same time, from Bernie Sanders to Podemos: free-market ideology robbed them of security and prosperity, leading them to demand radical answers.

That isn’t going to change: and that’s why the left is going precisely nowhere. Why, at the very moment our ideas have been consecrated as the party’s mainstream, would we perform hari-kari? That remains the success of Corbyn and his supporters and cannot be airbrushed from history despite the undoubted attempts to do so. As it was under Attlee, Hugh Gaitskell and Harold Wilson, the left is a legitimate power within the party again, one which cannot be ignored.

Starmer has committed to the policies long advocated by the left; and so the left’s role now is to act as the protectors and defenders of those ideas, to ensure that those red lines are not violated, and to develop a vision of what post-coronavirus Britain will look like. The left may have succeeded in giving otherwise cautious Labour politicians the courage of their convictions again, but pressure must be maintained to ensure this remains so. While the left has understandably expended much energy on electoral politics in the past five years, in post-pandemic Britain there must be a revival in extra-parliamentary struggles – from the climate emergency to workers’ rights – to build popular support for a decisive rupture from a broken status quo.

Unlike most Labour leaders, Starmer’s politics is rooted in extra-parliamentary politics: those instincts should be appealed to. Those who hoped that a Starmer triumph would end the remorseless attacks from the rightwing media will soon be disappointed: it will fall to the left to push back against them. And while many Labour MPs, for a time, will be relieved that their Corbynite nightmare is over, the party’s right went for Gordon Brown and Ed Miliband as well as Corbyn. They will come for Starmer, too: the Labour leader may find his only genuine defenders are the left.

Starmer has many challenges, not least winning back older voters who have abandoned Labour. But the left should wish him well; the quid pro quo is Starmer stands by his promises. Now is the time for critical friendship, to wish a genuinely decent and progressive politician well: because his success is our only chance to rid the UK of the cruel injustices that both scar and define our society.

• Owen Jones is a Guardian columnist