Against the backdrop of the Tories’ historic European elections clusterflop, Labour’s results were merely bad. The natural party of government saw its vote share eroded by the Brexit party so badly that it was forced to endure its worst performance at a national election since 1832. Tory leadership hopefuls, looking to placate the infuriated Conservative grassroots, are already butching up talk of a no-deal Brexit, an outcome that parliament simply will not tolerate.

The Tory party would split if it pursued a soft Brexit deal with Labour votes; it would split if a new leader ran on taking Britain out of the EU to trade on World Trade Organization rules. Brexit represents a fundamental crisis for the governing party. It’s important to make this distinction, not to excuse the poor showing of Jeremy Corbyn’s party, but to emphasise that Labour, unlike the Conservatives, has a way out of its Brexit bind.

The problem for the Labour party has been how to juggle the conflicting political values of the electoral coalition it has, and the electoral coalition it needs for a majority. The attempt to broker a soft Brexit compromise was a noble, if doomed, enterprise. The Labour frontbench tied itself in knots over the precise calibration of institutional arrangements with the EU that would upset everybody a little bit, but not enrage half the country a great deal. But Brexit, since the 2016 vote, has become entrenched as a polarised conflict about values and political culture, rather than trade or economics. Any compromise on implementation is viewed as a compromise on integrity.

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It’s no good blaming the electorate for failing to understand your Brexit strategy, when the hedging of positions looks evasive and faffy. After losing 13% of its vote share to the Brexit party, Corbyn, John McDonnell and Diane Abbott have all signalled a strong pivot towards a second referendum to win back the 39% of Labour’s 2017 voters who switched to the Liberal Democrats and the Green party. Emily Thornberry, the shadow foreign secretary, went further and pinned Labour’s poor performance on its failure to campaign for remaining in the EU.

A remain-oriented turn in strategy comes with potential drawbacks. The most obvious is that 78% of Labour’s target Tory marginals voted leave in 2016. And it’s not unreasonable for those voters to expect the result of a referendum that they voted in to be implemented, whatever the #FBPE Twitter account might say.

But there’s also a deeper issue at play. Labour isn’t merely a progressive party for civic-minded individuals: it’s the deepest expression of a workers’ movement that the country has. The nature of class composition and industrial organisation has changed a great deal since the party was founded 119 years ago, but a decisive shift towards being the electoral vehicle for socially liberal metropolitan voters represents a substantial – and undesirable – transformation in Labour’s soul.

But maybe the Labour left doesn’t have to become “Blairism-but-with-UBI” to survive. Corbyn’s failure to embrace Europhilia during the 2016 referendum was blamed by many for remain losing the vote. Yet I think there was an honesty about his claim that his support for the EU was a “seven or seven and a half” out of 10. Because really, apart from the people who paint themselves blue and yellow and stand bellowing outside the Palace of Westminster, who feels 100% in favour of the political direction of the EU?

Play Video 1:15 Jeremy Corbyn reacts to Labour losses in EU elections – video

As someone who voted remain, I look at some of the EU’s greatest hits – the crippling austerity measures imposed by the troika of the European commission, European Central Bank and International Monetary Fund on Greece, the bloody borders of Fortress Europe, the institutionalisation of neoliberal ideology – and worry that my vote was interpreted as a mandate for the continuation of those horrors.

A dash of Euroscepticism in a campaign to stay in the EU needn’t be a demobilising factor; it’s grounds for strong leadership in reviving popular consent for EU membership.

An uncomfortable fact for leave supporters on both the left and right is that the EU has not been the main cause of Britain’s regional inequalities or austerity measures. The problem, particularly with EU state aid regulations, has been how UK governments have chosen to interpret EU rules. Most of the barriers to implementing a manifesto on the radical edge of social democracy have to do with the constraints of domestic politics, rather than transnational governance.

It is the case, however, that even when spending decisions taken by national governments fall within EU deficit-reduction targets, they have been threatened by disciplinary measures. It’s reasonable to suspect that if Labour wanted to pursue a policy platform that was more interventionist than its 2017 manifesto, it would soon come into conflict with the EU. I say bring it on.

Britain has historically had a strong position within the EU by virtue of its status as a former imperial power, enjoying opt-outs on the Schengen travel rules and the eurozone that few others have been granted. It’s always been half-in, half-out – a state of affairs that has been most effectively weaponised by rightwing Eurosceptics. Labour has been unable to bring together leave and remain voters by synthesising a soft Brexit position. And it can’t throw its lot in with the no deal brigade and maintain a claim to protecting the economic interests of working-class people, or indeed taking an ideological stand against the far right. Instead of disavowing its own agency when it comes to the EU issue in UK politics, Labour could find itself breathing a second life into the remain and reform agenda on the European stage.

There’s much to be said for being rule-breakers and not rule-takers in Europe. Rather than accepting the constraints of Labour’s electoral tightrope walk, Corbyn could set out a vision of EU membership, with a fightback on limits to the UK’s economic autonomy. A commitment to remain should come with a solemn promise: if aspects of a future manifesto come into conflict with EU rules, then screw it, Labour will happily have that fight. And this isn’t just a PR exercise, it’s a push for political change.

As Labour MP Lloyd Russell-Moyle says, “much is done in [European politics] by a show of strength, determination and willing to go to the line – we could lead the rebel charge to transform the worst bits of Europe and keep the bits of EU democracy and socialism we have already achieved”.

A remain campaign is no longer about continuity, an affirmation of neoliberal values at the expense of workers’ struggle. It’s an expression of the conflict between the freedom of people and democratic institutions, and the freedom and protection of capital.

• Ash Sarkar is a senior editor at Novara Media