The nation’s focus is all on Brexit as a Tory soap opera: 48 signatures from the 1922 committee, a few big cheeses from the CBI, away days at Chequers. On the other side, there is this amorphous mass, “the people”, their views registering only in their millions, their protests reported as spectacle. The soap opera hots up when one of its characters says “scrap the Good Friday Agreement”, or “get pensioners to pick fruit”. The people get spooked when they’re told to stockpile food. The plot doesn’t move forward because the Tories can’t even agree a plan to take to the EU. People are endlessly polled on a series of repetitive and incomprehensible options, then commentators wonder why they don’t budge.

The opposition has so far played a minor role. Labour’s ambiguity seemed strategic in 2017, and paid off. It promised to respect the referendum result, yet at the same time assured a “jobs-first Brexit”. It was enough to placate the leavers, while assuring the remainers that nothing diabolical would happen.

The intervening months have shown this to be a fantasy. The softest possible Brexit is simply to accept the old rules with new impotence; any other Brexit would be economically painful, and to what purpose? To execute a project born of an ideological battle between the free-market right and the far right. Brexit corresponds to no Labour values.

In the beltway of Westminster, too much emphasis has been put on shifting the leadership from the top. Even if that were possible, changing the minds of five guys in a room could never represent the rewilded, pluralistic democracy upon which the current Labour project is founded. Pressure to remain in the EU can only come from the grassroots, otherwise it is the elite conspiracy, its critics decry. But the important thing missing from the analysis is that this grassroots movement already exists: constituency Labour parties, trade union branches, local Momentum groups and the broader left – steel workers in Hull, migrant workers within the NHS, and NHS staff more generally, Women Against Brexit – all working in ways both coordinated and spontaneous to stop Tory Brexit.

The remain campaign was dominated by the establishment Stronger In group. Its defining tactic was Project Fear, spearheaded by a cross-party coalition including George Osborne and Alan Johnson. It drowned out grassroots left campaigns such as Another Europe is Possible – led by the academic Luke Cooper and the activist Michael Chessum, who also organised the Stop Trump march. The case they made wasn’t about single markets, export tariffs, tailbacks on the M20, even food shortages. It was about the EU as the only set of institutions ever built on the principles of peace and reconciliation, rolling back the nationalist tide; one of very few capable of the kind of collective action – on climate change, the rise of fascism, workers’ rights and taxation – by which the social conquers the corporate.

The EU looms now as this technocratic body, dominated since Margaret Thatcher by the interests of capital – but those were not its roots, and will not be its future. From the group of European socialists who drafted the Ventotene manifesto – a vision for a united Europe – in the 1940s, to Jacques Delors’ social chapter, European federalism was conceived to avoid war, foster equality and build social solidarity. Many of the leftwing critiques of the present-day EU are fair, but are the product of the UK pulling the EU rightwards. To walk away on a Lexit basis is not just uncomradely, it’s a little bit rich.

Labour leader Jeremy Corbyn. Photograph: Murdo Macleod/The Guardian

Speaking practically, the only orderly way now to avoid Brexit is via a Labour government. The Conservatives will not come to their senses; a centrist party would be a pipe dream even if it had any ideas; the Liberal Democrats would need a bounce that would put them on the moon. And there is a nobler truth beneath these gritty psephological realities, which is that the vote to leave the EU was a vote for discontinuity. Leave areas map almost exactly on to those hardest hit by austerity. Whatever your views on Jeremy Corbyn the man, you would acknowledge, I think, that his is the only party that promises radical change. To overturn leave with no plan to overcome the economic conditions beneath it would be acting in bad faith. To accept leave knowing that those conditions would only deteriorate in the wake of its recession would be worse.

In the immediate aftermath of the referendum, it was by no means plain to us that remain was still a legitimate argument, and yet the leave plan was so flaky, so narrowly won, so riddled with nefarious associations that have since come into focus – racist advertising, Russian troll bots, lying, cheating, dodgy data – that to surrender to it seemed like an abnegation of civic responsibility. It became obvious that demos and pamphlets were necessary but insufficient. Deeper democratic channels had to make the case, in concert.

This is where the unsquarable circles emerge: the legitimacy of the left’s grassroots organisations begins and ends with listening to their members. At an event in Birmingham last month, organised by Another Europe is Possible, there was a passionate man from Unison, Ravi Subramanian, who described the impact of Brexit on his mainly female members, predominantly low-paid and precarious. Yet since their summer conference hadn’t passed a motion on it, he couldn’t – even as he described the catastrophe – come out trenchantly in favour of a vote on the final deal.

Momentum members, likewise, are among the most solid defenders of migrant rights you could find. Stopping a Tory Brexit – as one member’s petition demands – could not be a more natural stance. Yet for Momentum to take a remain stand now could only come from members, which raises a key impediment: loyalty to Corbyn and passion for remain have been ranged against one another, mainly by the activities of Labour’s selfidescribed centrists. Chuka Umunna, Alastair Campbell and Chris Leslie are perceived to be fighting Brexit with the agenda of taking Corbyn down with it.

Another Europe is Possible has spent the summer persuading constituency parties to bring a motion to Labour’s annual conference this September calling for the party to oppose Tory Brexit. Two hundred constituency parties are debating the motion, but the number of sheer man hours spent discussing how this can happen without undermining Corbyn is incredible. Corbyn versus remain shouldn’t be the choice: nobody should have to renounce their values just because someone else is wearing them for different purposes.

Nonetheless, the institution already exists in this country by which people can avert disaster: it’s called the Labour party. Its stance isn’t going to change as a result of Westminster shenanigans. If and when remain comes back on the table in some or other form, it will be because the grassroots left found its power.

• Zoe Williams is a Guardian columnist