Long before the EU started to evolve into its current incarnation, there was a different vision of a united Europe. In 1941 a group of socialist and communist anti-fascists were imprisoned by Mussolini on the island of Ventotene. Led by Altiero Spinelli, they produced the Ventotene manifesto, a strategy for a united socialist Europe as “the only way out of their common predicament of domination by Hitler”.

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Today a new “common predicament” – austerity and corporate-driven markets – means this socialist European tradition must be revived in a modern, pluralist form. It is needed to counter the decline of social democratic parties across Europe, where only the Portuguese Socialists under António Costa and Jeremy Corbyn’s Labour have bucked the trend.

While Corbyn opposes the neoliberalism of the current EU, he has pledged to work for an “anti-austerity Europe”, most recently last month at the Durham Miners’ Gala. This is more than a rhetorical flourish: it is a signal that Corbyn is more pro-European than the press conveys, albeit not in the conventional way. His recent statements on Europe clarify that being in the EU does not necessarily prevent public intervention in industry, and highlight his commitment to European social regulation.

And there is significant support for these regulations that crosses the remain-leave divide: 73% of the public either support the working time directive or feel it should go further, while 73% also back a bankers’ bonus cap and 82% oppose any lowering of food safety standards. Leave-voting trade unionists at the Durham Miners’ Gala told me they do not want to lose regulations covering employment protection, food safety and health and safety at work.

So there’s a popular alternative to either a deregulatory, free-market Brexit or being part of a neoliberal EU: a new relationship between an anti-austerity Britain and an anti-austerity Europe. As a strong supporter of Corbyn, I urge him to work with the Portuguese and Spanish governments, as well as labour movements and left parties across the continent, to map out a collaborative strategy for a socialist Europe, both through membership of the EU and through strong support for labour and social movements across Europe.

Facebook Twitter Pinterest ‘Corbyn could champion an integrated European railway system.’ Photograph: Claude Paris/AP

British governments have been at the forefront of turning the EU into an instrument of market politics, from opting out of key elements of Jacques Delors’ European social charter (attacked by Margaret Thatcher as “socialism by the back door”), to David Cameron’s veto of the financial transaction tax. The way forward for the left is not in “stopping” Brexit. Instead, it lies in working with allies across Europe, for example by supporting the new Social Democrat German finance minister, Olaf Scholz, in putting the transaction tax back on the table; and backing measures to end the undercutting of wages and labour rights, by requiring companies employing migrant labour to respect the union and wage agreements of the host country. In the same way that New Labour once shifted European social democracy to the right, Corbyn’s Labour could shift it to the left.

Labour has developed impressive national policies for publicly led economic development that would address the inequalities that underlie support for Brexit in the north of England. Why not extend these principles of public productivity on a European scale?

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Public ownership of the railways, for example, could enable Corbyn to champion an integrated, reasonably priced and publicly owned European railway system, providing an alternative to airport expansion and a way of taking freight off the roads. Other Europe-wide applications of Labour’s 2017 manifesto commitments could be developed by bringing together decentralised city-run public companies for renewable energy, and expanding the co-operative sector – both of which already have considerable support across Europe.

An anti-austerity vision can provide a framework for a new relationship between the UK and Europe. Of course, a new relationship must address trade, but the question is what frames and drives trade policy: market competition, or meeting social needs, where market exchange is subordinated to a framework of public and co-operative ownership?

The clash over EU membership has so far failed to produce a constructive debate. The two sides have simply shouted past each other. Instead, we should be aiming for a debate that generates the engagement with pan-European issues that has been long absent in Britain. Labour is uniquely placed to achieve this as its membership and voting base brings together people from both sides of the Brexit debate.

This spirit of creative debate is already evident in the bottom-up processes that are feeding into Labour’s new economic policies. The first stage for developing a new relationship with Europe, after clearing away the debris of Theresa May’s broken Brexit plans, must involve argument and debate across the Labour party and Momentum, and its allies on the European left.

A new politics, based on a belief in the extraordinary capacities of ordinary people, requires breaking from the presumption that the people can only say yea or nay to the proposals of the political class. Britain’s future relationship with Europe should be discussed in neighbourhood and town meetings across Britain. To build a Europe for the many – one that lives up to the Ventotene vision – the many must be actively involved in its creation.

• Hilary Wainwright is co-editor of Red Pepper and research director of the New Politics Project of the Transnational Institute, Amsterdam