The People’s Vote march showed it’s not just leavers who are angry and patriotic

So was the People’s Vote march really a game-changer, and, if so, how much of the game did it change? Certainly, it was large: an estimated 700,000 people, the “second-best attended demonstration of the century,” organisers said. The prize stays, of course, with the march against the Iraq war in 2003, which looms like a cloud, ready to rain on every subsequent parade: if a million people can’t change an outcome, why should any government react to any fewer?

And yet Saturday’s demonstration changed the weather, knocking sideways the now prevailing idea that leavers are angry and determined, while everyone else only wishes for a competent person to just sort Brexit out so we can stop talking about it.

Remainers are also angry and determined; also patriotic; and more convinced than ever that there is no available Brexit, on paper or in anyone’s wildest dreams, that delivers to their country anything but hardship, disempowerment and hassle, in varying proportions.

The endless bother – civil servants running about to produce agreements exactly like the ones we already have, or manufacturers figuring out new ways to do the same thing while clearing bureaucratic hurdles – sounds like the most trivial downside of the three, yet it’s the one that so far has interrupted all other business of government the most, and dissolved, perhaps permanently, the image of the Conservatives as a safe pair of hands. By March 2019, it is hard to imagine a single public service, from the NHS to prisons, from schools to social care, that will not be in crisis. My favourite banner read: “Please stop. You’re ruining everything.” Most statements have to be amplified for impact, and flattened out a bit to fit on a placard; this simple, unadorned message is literally true.

Unable to write it off as small fry or violent, critics have instead concentrated on the composition of the march. The charge of middle-class-ness fits as comfortably into the arguments of Lexiters as it does Brexiters: anti-EU proponents from left and right both cast themselves as defenders of the “left behind”, heroically battling the faceless institutions that have stripped agency from ordinary citizens. In this discursive context, anyone found arguing against Brexit, who does not themselves qualify as “left behind”, is explicitly allying with the elites against the masses, willing a return to the pre-2016 status quo, disavowing their responsibility to their less prosperous countrymen.

There was, certainly, evidence of the middle classes on the march – more than one banner mentioned brunch, which in signifier terms is the food equivalent of “latte-sipping”. It is true too that there are people at the centre of the remain camp who wish, more or less explicitly, for a return to the normality of our old post-political landscape, where nothing was ideological and all decisions were no more or less than any reasonable person would make.

What’s missing from this symmetrical analysis is what’s staring everyone else in the face: Brexit, in its rhetoric and all its iterations, is a far-right project. Explicitly and stridently anti-immigrant, it nevertheless is happy to accommodate rich migrants: the word “skills” is used, transparently, as a proxy for salary, giving us a brave new world in which an early-career banker has higher skills than an academic with three degrees; and any given MP has almost twice the skills of the most qualified nurse.

Reorganising the value of citizens by their wealth would have been unheard of even three years ago. Brexiters propose to meet the financial challenges of the future by curtailing workers’ rights, and the trading challenges by dissolving regulations. It is a programme of systematically rebalancing power – towards the wealthy, the employers, the mass producers, and away from the workers, the consumers, the ordinary citizens – such as no party would have dared to suggest in any ordinary manifesto. All progressive sinews should strain against it, and not care whether this puts them on the same side as Anna Soubry or Labour centrists.

The existence of Liberal Democrats on the demo does not make it the march of the comfortable elites: it neither undermines nor neutralises the Love Corbyn: Hate Brexit brigade.

Rejecting the aspersions cast over its legitimacy, the real question about this protest is practical: if it could influence our course on Brexit, what would that look like? Will it be a subtle effect, in which growing numbers of MPs start to express a duty to their remain constituents with the same commitment as colleagues do in leave areas? Or will it be a more seismic shift, in which Labour changes course, rescinds its promise to deliver a better Brexit, and becomes explicitly the party that will take the decision back to the country?

The march itself doesn’t scotch the idea that Labour can negotiate its own deal (though that, on time constraints alone, is fanciful): but it does capsize the raft that’s been keeping its resigned ambiguity afloat. Remain might once have looked like an elite conspiracy against Corbyn and his agenda of radical change: now it looks like a grassroots social movement coalescing to fight a chaos that was created by the Conservatives and serves nobody’s interests but theirs.

Finally, is it right for a large demonstration to make a difference? As sociologist Will Davies points out, in his recent book Nervous States: How Feeling Took Over the World, no march is representative in any real sense: “If crowds matter at all, it is because of the depth of feeling that brought so many people into one place at one time.”

It would be a blunt tool indeed to lob the country’s destiny to whoever had the best turnout. Theresa May could ignore the call for a people’s vote, in the proud tradition of governments since marching began, if she had unity, focus or parliamentary numbers on her side. But in the absence of those things, all she has herself is the “will of the people”. It is a dangerous thing to rely on – frangible, mutable, arguable, and beset, always, by the question: which people? Whose will?

• Zoe Williams is a Guardian columnist