Brexit is the rock on which our democratic system has run aground. But really the ship has been holed beneath the waterline for some time.

Some are content to shuffle the deckchairs and simply replace one captain with another – which may be necessary but is far from sufficient. Yet we can’t just stop Brexit and press the rewind button. Nothing will be the same again. And depending on the lessons we draw from the crisis and the actions we take, things will either get a whole lot better or a whole lot worse.

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What we are witnessing is not a democratic blip but the breakdown of a largely industrial form of democracy in an age of digital networks. The metaphor to work with is the factory v Facebook. In the world of the factory, we all knew our place – as worker, owner or management. The factory, or Fordist, model wasn’t just how we made cars, but how we won wars and ran governments. A technocratic elite decided what was right for us, we knew our place and we did, largely, as we were told. The political fight was over the levers of change.

Today’s world is much more akin to Facebook. We are all interconnected and can know, join, leave and decide, individually and collectively. Of course we have to challenge the ownership of such a system, but the culture of participation and collaborative action it enshrines defines the age and seeps into our bones.

But Britain has a particular problem. Its adversarial, two-party monopoly system exacerbates social and political polarisation. If we had proportional representation, we might never have had the conditions that led to Brexit. It is precisely because a few swing voters in a few swing seats are the only voices that matter that a majority can be simply ignored and marginalised. It’s a system that leaves millions feeling left behind.

So when David Cameron, as prime minister, called the referendum in 2016 he in effect gave huge numbers of disenfranchised people their own megaphone through which to shout out their anger and humiliation. It was a demand for far-reaching change.

Many people regret that the vote happened, believing it somehow unleashed undemocratic, unfair or ill‑judged views. As a democrat, I don’t. Of course both sides abused the referendum process, but the pressure valve released a lot of pent-up fury, and it has allowed us to deal with that. We shouldn’t run from this demand for change: we should run towards it. More than anything, the change demands a new form of democracy, not just a change of government.

That’s because if the old mechanical levers no longer work, it doesn’t matter that much who pulls them. And if the system no longer allows us to solve economic or climate injustice, then the doom loop is complete, as people either give up entirely or look for populist and authoritarian answers. No political party has won a working majority since 2005, and none looks likely to, because no majority can run a democracy built for the past not the present – let alone the future.

Facebook Twitter Pinterest Samuel House, part of the Haggerston and Kingsland Estate in London. Photos of residents were placed over the windows of empty properties as part of the I Am Here art installation. Photograph: Mike Kemp/Corbis via Getty Images

Brexit, globalisation, mass immigration, climate change, the rise of the robots and more can’t be fixed using the old democratic tools of technocratic command and control: a politics where one side beats the other to implement its plan. Indeed, beyond left and right, other uncomfortable divides are opening up – between town and country, liberalism and authoritarianism – that are complex, and cut across traditional divides.

Not only that, but through social media we have the means, at our fingertips, to express our diverse and fast-shifting views and moods. The complexity of today’s society, of power that is both digital and global, demands a politics of collaboration, not competition. It tells us that the future will be negotiated, not imposed.

As such, representative democracy will only be buttressed if other forms of democracy, direct and deliberative, are put in place. That is why many people, including myself, have called this week for a Brexit citizens’ assembly. It’s a simple and compelling idea that could break the logjam of a parliament that isn’t built to represent the ways in which the UK now divides, allowing instead for a form of reasoned politics to get us out of this mess.

The way it works is that a random but representative group of citizens is given impartial evidence in order to recommend, in this case, no deal, or a deal and its shape, or a second vote and the question. The practice is used widely and successfully around the world for questions politicians can’t or won’t answer – most recently in Ireland on abortion.

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But why should millions of voters hand over a decision to a few hundred? The answer is, this isn’t about numbers but finding a national consensus. A growing number of MPs know parliament can’t deliver this on Brexit, and want a way out.

A citizens’ assembly is therefore a solution to the Brexit impasse. But, just as important, it could lay the foundations for a new form of democracy that allows more meaningful participation. Calm, reflective and empathetic, it is everything our politics currently isn’t. Because this isn’t just about new democratic structures but a new political culture where it’s safe for politicians to say “I don’t know”, “it’s too complex”, or “I need help”. Our awful, adversarial and macho political culture is simply no match for a world that is complex, grey, nuanced and paradoxical.

The democratic genie of the 21st century is out of the bottle, and it isn’t going back. Brexit exposes the inadequacy of our political structures and culture. Whether we leave or remain really matters; yet what matters more is how we do any of it. The way out of this mess has to be more democratic that the way in.

• Neal Lawson is chair of the pressure group Compass