For many in the Labour movement, the socialist, diverse left bloc of last week’s Put it to the People march may have felt more of a political home than, say, the main, continuity remain element – and that also highlights the big Jeremy Corbyn-shaped hole both at the event and in the wider campaign. For it actually to be more Corbyn left, the campaign would need the leadership’s buy-in (and the grassroots organising that would flow from that). Instead, it was down to the left bloc of Love Socialism Hate Brexit MPs and campaigners to present the radical left, anti-racist arguments for a second referendum. They did a great job, even though their message did not necessarily chime with everyone: one organiser told me they overhead someone at the main demo ask why the left bloc kept going on about socialism at an anti-Brexit march.

This statement encapsulates the problem with a people’s vote campaign led by the centrist status quo that much of the leave vote was a protest against. Meanwhile, the anti-racist component of arguments over Brexit is too often ignored as we pore over the parliamentary politics of who might vote for which Brexit option and what happens next. Here we are with only bad choices, mounting chaos, reckless rhetoric, a terrible democratic failure and a febrile political climate, all of which is firing up a hate- and anger-filled far right already emboldened by Brexit. Whatever happens next, none of that is going away quickly.

But one credible progressive case against a second referendum is that it will set this toxic cocktail alight, sparking a backlash against the far right’s usual targets: migrants and minorities. Implicit in this is an admission of defeat: that the left could not face down such an outcome, nor mount a defence of the communities on the receiving end of it.

Clive Lewis MP said at the march: ‘There aren’t that many black MPs [in Labour] supporting Brexit … We could see that Brexit wasn’t going to end well for us.’ Photograph: Andy Hall/The Observer

Looking at the left’s current configurations, it’s hard to argue with that. Among those at the political helm of the people’s vote campaign are advocates of immigration controls who exacerbated hostility towards migrants by invoking “legitimate concerns” over the pace of change. The Labour leadership, meanwhile, abandoned a commitment to freedom of movement, even though this would by definition mean increasingly hostile border policies. In January, the party sparked a backlash when it tried to abstain on a horrendous Tory immigration bill. Then there is the Lexit caucus, a component of which is currently echoing an antisemitic conspiracy beloved by the far right, while claiming that liberals are in cahoots with ethnic minorities to thwart the wishes of the (always implicitly white) working class. If you are a migrant or from a minority-ethnic community, which bit of this picture is supposed to provide reassurance that the left has your back?

But this risks diminishing the strong BAME element of the people’s vote left bloc, at which half of Labour’s black MPs spoke. As Clive Lewis, the Corbyn-supporting Labour MP for Norwich South, said at the march: “There aren’t that many black MPs [in Labour] supporting Brexit … And do you know why? We’ve got a bit of a spider sense when it comes to shit like this. We could see that Brexit wasn’t going to end well for us.”

These Labour MPs and campaigners are not ignoring the toxicity of a second vote, the racist foghorn it would unleash or the upsurge in racist abuse that could follow. They just appraise another vote as the best (or least worst) way of facing down the prejudice and bigotry that Brexit unleashed – and of facing down this rightwing, free-market fundamentalist project altogether.

Some say that, whatever happens next, the far right is already emboldened. It feeds off victory, as it did when hate crime spiked after the first referendum. And it is fuelled by betrayal narratives, currently applied to soft Brexit, to Theresa May’s Brexit and to no Brexit at all. Hope not Hate activists report that, after years of canvassing in Ukip and BNP-supporting areas, they are taken aback by the open racism currently on display in leave constituencies.

Barring an election, the only Brexit option that offers the opportunity to confront racism and express support for immigration is a second vote. Shaista Aziz, a Labour councillor and one of the speakers at Saturday’s left bloc, says she is already having these tough-but-necessary conversations, at a time when public awareness of the Brexit mess is acute. Campaigners have noted that the Labour grassroots is, on the whole, more vocally motivated than the leadership and could be mobilised into spreading the pro-migration message.

For a second vote to stand a chance, it needs the socialist Labour leadership behind it, making it about transformational politics in Britain, rather than a default to a broken economic policy that is breaking people. But regardless of support for another referendum, with the far right permeating our political air supply, the Corbyn left must throw its intellectual, moral, campaigning and policymaking weight behind full-throated anti-racism and support for immigration. This is so long overdue, it’s starting to feel as if the left really has conceded defeat.

• Rachel Shabi is a writer and regular broadcast news commentator