The resignation of Theresa May, the rise of Nigel Farage’s Brexit party and the Tory leadership election have cast a sharp light on the choices confronting the Labour party. It appears that, notwithstanding frequent assertions to the contrary, the balance between leavers and remainers has not shifted much since the referendum. As soon as political leadership became available, leave’s mass support across England and Wales was reaffirmed, including in the working-class heartlands of Labour.

Farage spoke to popular frustration with the parliamentary shenanigans over May’s deal and the associated failure of democracy since 2016. It is deeply unfortunate that a rightwing populist has again been able to make inroads into the natural constituency of the left. His success makes it vital for the Labour party to offer fresh leadership, while maintaining its working-class roots. For that, Labour must not side with remain.

The demise of May and her deal is only partly due to the inherent complexity of Brexit. The main centres of economic and social power in Britain are determined to maintain the closest possible links with the EU single market and customs union. The City is the financial heart of the EU, seeking to operate freely in foreign exchange transactions, derivatives clearing, bond issuance and so on. The manufacturing industry, competitive in aerospace, pharmaceuticals, defence equipment and high technology, sees the EU as its terrain. Financiers and manufacturers have furiously lobbied parliament to avoid a rupture with the single market and the customs union. In the process the democratic will of the British people has been obstructed for two years.

For decades the political strategy of the British establishment had been to accept the position of net contributing member of the EU in exchange for significant “opt-outs”. That strategy came to an end when David Cameron was unable to secure “special status” in 2015-16. After the referendum, May attempted to reverse the strategy by taking Britain out of the EU, while “opting in” on issues that were important to big business. Her deal was intended to formally satisfy the demand for exit, while allowing British business to maintain close links with the EU. She failed because – in addition to her political maladroitness – the British political system is in deep crisis and cannot fulfil even its basic functions.

The most important aspect of this political crisis is that the Tory party has practically ceased to speak for the interests of British big business. Justified concerns about sovereignty in the EU have assumed a life of their own, taking a firm grip on the nationalist wing of the Tories. From the standpoint of the establishment, things became even more volatile after Jeremy Corbyn shifted the Labour party radically to the left. In that context, May’s minority government never stood a chance.

Farage has marshalled the anger of leavers but cannot offer a way out because his party lacks even a basic programme. What he has done is to force the candidates for Tory leadership to adopt the language of “hard” Brexit. Yet the new leader will inherit an insoluble conundrum due to the divisions of the Tory party and the unchanged Commons arithmetic against no-deal Brexit. Florid phrases will be of little use. As 31 October approaches, another sharp political crisis is likely to emerge that may well involve calling a general election.

It is not surprising, therefore, that the battle for the soul of the Labour party has commenced again, especially after its poor European election results. The worst outcome would be for Labour to become openly wedded to remain. That would detach it from its historic roots, ruin Corbyn’s socialist project and directly undermine his personal position as leader. It is also likely to destroy Labour’s electoral support in precisely the marginal constituencies that the party must win, a point powerfully made by 26 Labour MPs in a letter to Corbyn. The final nail in the coffin would be for Labour to advocate revoking article 50, which would be an insult to democracy and a huge national humiliation rolled into one.

The radical change promised by Corbyn is impossible to achieve within the regulatory structures of the EU. These structures are designed to serve the interests of big banks and large corporations. Brussels would not tolerate socialist policies in the UK (or anywhere else). It would use its extensive powers to undermine them, in cahoots with domestic British interests, thus also impeding the democratic renewal of Britain.

As for “remaining and reforming” the EU, this is a wild goose chase. EU institutions are designed to be impervious to expressions of popular democratic will. Any treaty reform would require unanimity among member states, while any reform via secondary legislation would need the consent of the commission, the majority of governments and the majority of MEPs, before jumping the hurdle of the European court of justice. There is just no chance.

Britain certainly needs a fresh start, and its people demand it. The radical transformation promised by Corbyn – especially to the young – is possible only if Labour does not become attached to remain. The party must continue to honour the referendum result but should also be bolder in airing the radical possibilities offered by leaving the EU. So far Labour has been reluctant to do that, exuding confusion and allowing its rank and file to drift toward remain. It is not too late to correct the balance, if it wants power.

• Costas Lapavitsas is a professor of economics at the School of Oriental and African Studies (Soas), University of London, and a former Syriza MP

• This article was amended on 25 June 2019 to replace an illustration used in error. The image showed campaign pamphlets from the group Labour for a Socialist Europe, which does not support the views expressed by Costas Lapavitsas. On the contrary, the group – which includes Labour members, MPs, MEPs, trade unionists and other activists – is campaigning to stop Brexit.