Since its dismal showing in the European elections, Labour has been in an extended row about Brexit. Strikingly, this spat is specifically between sections of the Jeremy Corbyn-supporting left of the party.

On one side, its ranks swelled by those sobering election results, is the view that Labour’s loss of sizeably more support to the Liberal Democrats and Greens than to the Brexit party shows that the leadership should unequivocally back a second vote. Others reject this as a distraction, saying that backing remain now would wreck the party. Immediately after the EU election exodus, Corbyn pledged support for a referendum on any Brexit deal. Key allies John McDonnell and Diane Abbott also spoke forcefully in favour of a public vote. But the party leader has since rowed back, in a now familiar pattern – one Labour MP describes this as a “tug of war” between pro- and anti-referendum wings.

To fight on the terrain the party should be – it has to first reckon with the turf we are actually standing on

Labour’s European election drubbing has brought to the surface rows that having been rumbling along for some time. Chunks of the Corbyn coalition within the union movement, membership and shadow cabinet have urged the leadership to firmly back a public vote – saying this is electorally smart but also the right thing to do. Brexit is a free-market fundamentalist project that will harm the working people Labour is supposed to stand for. It is also the UK iteration of ethno-nationalist populism, and opposition to that is in Labour’s DNA.

The counter argument holds that Labour should fulfil the 2016 referendum mandate to leave the EU and not pick sides in this bitter national split – and that most of the seats it needs to win a general election are in leave-voting areas. It’s reasonable to say neither side relishes the prospect of another poisonous referendum. Many supporting a second vote view it as the last available, or least worst, option.

But what’s striking about recent expressions of the anti-referendum position is the language and tone. It’s not just an articulation of policy or strategy, but an accusation of abandoning the working class, levelled at left allies united in the desire to see a Corbyn government. Those supporting a public vote are cast as domineering, middle-class Londoners and “leftwing intellectuals” sneering at “ordinary people”, and who are shunning the notion that, morally, the Labour party exists to “represent the interests of working-class voters”.

The suggestion that Brexit was fuelled by working-class voters has been comprehensively debunked. In any case the working class is patently not homogenous, and certainly includes “ordinary” BAME people and EU citizens who do not support Brexit. Meanwhile, it is clearly the case that, sector by sector, Brexit will badly impact workers. If you factor in the unsettling undertones of rightwing populism in the invocation of metropolitan intellectuals thwarting the wishes of working people, there is a sense of an increasingly messy tussle over the core values of the party – which is precisely the bit of Brexit that the Labour leadership has sought to sidestep up to now.

It’s reasonable that supporters of the Corbyn project would not want to upset the disparate coalition of Labour voters that could get him to power. He represents a once-in-a-lifetime opportunity for a left-led Labour government to tackle decades-long inequalities in Britain, with a concrete and radical socio-economic programme. But this position involves a little shoulder-shrugging over our departure from the EU (which, after all, has its faults). But then you may find yourself pandering to supposedly “legitimate concerns” over immigration, indulging erroneous claims about EU workers undercutting wages, and abandoning freedom of movement. You may also, along the way, be acquiescing to clamours to enact the “will of the people” – a majoritarian narrative set up to breed a toxic sense of betrayal.

Before you know it, Britain has left the EU and a nativist right could be emboldened and surging. By this point, you might start wondering what it is that Labour is fighting for.

Corbyn’s leadership has from the start been under constant attack, impairing a capacity to calibrate criticism. When the Corbyn-backing TSSA union ran surveys that foretold – pretty accurately – the dismal European election results, it was not given weight. The calculation throughout has been that remainers would stay loyal to Labour come what may, but the European election confirmed what polling has been signalling for some time: this is not necessarily the case. At some point, the gulf between voters’ values and party position grows too great and a rupture ensues.

Corbyn pledges Labour will back referendum on any Brexit deal Read more

The question now is whether a Labour pivot has come too late. If the leadership is reluctantly bounced into backing a public vote, but then doesn’t engage in leading a campaign to support it, the chances are we’ll end up in the worst-case scenario: securing a referendum only to lose it. There is little point adopting this position without jumping into the political space it creates – filling it with frank conversations about Brexit, from economic impact assessments to a principled defence of free movement.

This won’t be easy: Labour campaigners and MPs describe long and agonising door-to-door discussions with people who are justifiably angry and feel abandoned by politics. But this switch is the missing element depriving Labour of a springboard from which to launch the conversations it really wants to have: creating a transformative socio-economic agenda, a green industrial revolution, regional investment policies, plans for reversing austerity and healing divisions in society.

In other words: to fight on the terrain where the party should be it has to first reckon with the turf we are actually standing on, over Brexit. Not least because, increasingly, Labour politicians, members and voters sense that it is ultimately all the exact same fight.

• Rachel Shabi is a writer and commentator