On 4 November, as the government plans further attacks to maintenance grants for the poorest students, the student movement will hold a national demonstration for free education. It will mark the fifth anniversary of the student movement of 2010, when the occupation of Conservative party offices at Millbank Tower triggered one of the biggest mass movements in recent years. More than 100,000 walked out of classes and blockaded city centres. Dozens of university campuses were occupied. When the vote to triple tuition fees narrowly went through, 30,000 of us held a protest that was audible inside parliament, burning benches to keep warm in the police kettle.

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Even then, with the nation watching, none of us imagined that we would be joined and endorsed by the leadership of the Labour party. In the wake of the Liberal Democrats’ tuition fee U-turn, that era was characterised largely by its crude anti-politics, as well as its press-friendly lines about intergenerational injustice and conflict. Throughout the subsequent five years, the recurring theme for those of us trying to oppose austerity was the total failure of the official institutions of the left – major unions and the Labour party – to support grassroots movements. The National Union of Students opposed the mobilisations of 2010. Movements ebbed, flowed and linked together, but, lacking any form of political expression, were easily demoralised and marginalised.

At a stroke, Jeremy Corbyn’s election has given Britain’s anti-austerity movements the biggest weapons of all: hope and credibility. From this perspective alone, Corbyn really does represent a new politics; no other Labour leader in history has been this connected to social movements. When the student movement mobilises on and after 4 November, its demand for free, accessible education won’t be a pipe dream; it will be the official policy of the leader of the opposition.

Facebook Twitter Pinterest ‘Corbyn’s victory is actually a product of the social movements of 2010 and thereafter.’ Photograph: Mark Thomas/Rex Features

The relationship between Corbyn’s project in Labour and movements in the streets will not be one way. As well as sharing a deeply held belief in the causes they represent, Corbyn knows that linking up with grassroots campaigns – from workers’ struggles, to housing campaigns – is the only way he will be able to hold on in Labour and win in 2020. A new mass movement must form the backbone of his electoral strategy. And in contrast to the fixers and triangulators of the labour establishment, what these movements and Corbyn have in common is their willingness to flout the political consensus – to propose bold, popular social reforms. A free education system with decent student support, public ownership of utilities and railways, tax justice and a fully public NHS are long-held commitments of Corbyn’s, but they are on the agenda because they have been put there by protest.

Corbyn’s victory is actually a product of the social movements of 2010 and thereafter. The student movement of 2010 may have been anti-political – and it would be absurd to claim that it made the weather on its own – but it did crystalise the mood of anger and injustice in the wake of the 2008 financial crash, and it kickstarted the anti-austerity movement. It is that mood that made Corbyn possible, and, more than that, it is the same generation of young radicals who have constituted much of the Corbyn surge.

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Like many generations before it, the radicals of 2010 and just after have compromised in order to become relevant – but unlike previous generations, they have not had to shift towards respectability and the economic right. In order to come to political fruition, this generation has had to ditch its anti-politics and, yes, much of its generational politics. It may have returned in a new form – its base in the new precariat, its politics built on the struggles of migrants and feminism as well – but it is the return of mass class politics that is channelling itself through Corbyn. Since 2010, the crowd that stormed Millbank Tower, and the crowds that joined them in the streets, have shifted left, not right.

The task for everyone on the left – working on unfamiliar ground and carrying one of the greatest responsibilities we will ever carry – is to establish a new mass politics. Whatever it consists of, this new politics will be dismissed by the rightwing commentariat as an anachronism, but it has already begun to win its place as “the new politics”. As well as being popular – progressive taxation, public ownership, new social housing and a living wage all carry public support – much of it is new and has never made it into the mainstream before. An education system that is free, democratised and accessible to all, an exploration of new forms of common ownership proposed by the shadow chancellor John McDonnell – this is the manifesto of a genuinely new social and political movement.

This force – if it can bring Corbyn’s supporters into social movements, if the new Labour leadership unflinchingly backs these movements in the streets – is capable of transforming much more than just the Labour party.