Four years on from the formation of the coalition government, the politics of austerity – along with its systematic marketisation of public services and its scapegoating of migrants and the unemployed – is in danger of forming a new common sense consensus in British politics. In a period that began with the student movement of 2010 and subsequent mass trade union mobilisation, the main upheaval in the bubble of mainstream politics has come not from the left, but from Ukip.

The anti-austerity movement will be marching again this Saturday. What matters is less what happens on the day than that the demonstration forms a focal point for revitalising the extra-parliamentary opposition to the programme of cuts and privatisation.

In the first 18 months of the coalition, the prospect of an anti-austerity movement capable of threatening the government's stability seemed real. By November 2011, students and mass trade union demonstrations had been joined by the public sector pensions strike, the biggest since the general strike of 1926, and Occupy put anti-capitalist sentiment into the headlines. This was the moment of the anti-austerity movement: it was direct action-focused, multifaceted and, crucially, ideologically diverse and open-ended.

The stagnation of this movement owed much to the failure of the traditional leftwing institutions to continue the fight and develop its anti-cuts slogans into a cohesive movement for an alternative to the market. When the pensions strikes petered out in early 2012, the unofficial networks of union activists and alternative organisations of the student left continued to mobilise, but faced an endless struggle with diminishing energy and resources.

This year, however, there may be a serious and concerted revival of resistance in the public sphere. On 10 July, a million workers will strike over local government pay cuts, and on 18 October, trade unions will again mobilise in the streets under the banner of "Britain needs a pay rise", as workers suffer the worse pay cut in real terms since records began. Meanwhile, following a historic U-turn at its conference in April, the National Union of Students has declared its support for free education and a coalition of groups is now coming together to call for a national demonstration, probably in November. If these days of action can spill over into a generalised wave of dissent and disruption, we may see a revival of the British left.

Any attempt to take this moment as a re-enactment of the 2011 anti-austerity movement, with the same ideological incoherence and reliance on often reluctant union leaders and politicians, will be vulnerable to stagnation. What is needed is a movement that proposes alternatives and which is built on a return to grassroots direct action politics. Looking at the line-up for Saturday's demonstration, one could be forgiven for thinking that resistance to privatisation and exploitation was coming primarily from leftwing celebrities and trade union general secretaries.

The past few years have given quite a different lesson: the most inspiring and important struggles in recent times have been bottom-up and rooted in a different approach. From Lambeth College, where teachers are on an all-out strike against new contracts that worsen staff conditions, to the 3Cosas Campaign – a vibrant campaign for sick pay, holiday pay and pensions at the University of London – to the Ritzy cinema workers' strike, a new kind of workplace activism is providing a template for future success, one based on unshrinking confrontation with management, not the odd one-day strike called for by central office.

These kinds of campaigns and unions – capable of engaging and organising young, migrant and precarious workers – are one of the great hopes for rebuilding a serious mass movement. In practice, this may have the effect of reasserting basic social democratic principles in politics but, ultimately, the outcome of the economic crisis and the ideological polarisation of the past few years point towards a more radical and unstable conclusion than a return to the post-war settlement.

The question remains how these fragments of a new left come together to state not just what it opposes, but what it is for. One thing is for certain: the chasm between the reality of what people think and the climate in the official media and political sphere is growing, on the left as well as the right. Polling consistently shows that on issues such as nationalisation and taxation of the rich, the public is significantly to the left of Ed Miliband. In order to prevent a post-coalition consensus among the political elite from becoming permanent, workers, students and the left need to go beyond anti-austerity and develop a narrative of the world we want to create – and this must become a movement driven from its base.