They promised sovereignty, but at first it was unclear which variety of sovereignty they meant. Were the politicians who swore we would regain it when we left the European Union referring to parliamentary or popular sovereignty? Now we know they didn’t mean parliamentary sovereignty. Boris Johnson’s government has sought to trick, rush, ignore and prorogue parliament at every turn.

“People v parliament” is Johnson’s pitch to the nation. So where do the people come in? If he is a champion of popular sovereignty, why does he propose no improvements to a 19th-century model of democracy that permits no popular engagement other than an election every few years, and a referendum every few decades? There is a tension between parliamentary and popular sovereignty. A lively, meaningful democracy would achieve a balance between the two. It would combine parliamentary (representative) democracy with participatory democracy. But no such balance is sought.

Rather than encouraging an informed, nuanced politics, Brexit has made our system even more adversarial

Representative democracy is a remarkably blunt instrument. Hundreds of issues are bundled together at every election, yet the vote tends to swing on just one or two of them. The government then presumes consent for its entire programme and, if it commands a parliamentary majority, for anything else it wants to introduce in its term of office. We don’t accept presumed consent in sex. Why should we accept it in politics?

I’ve often been asked, when I complain about a government policy, “So why don’t you stand for election?” This suggests that the only valid political role a citizen can play is to become a representative, so that only a tiny proportion of the population has a legitimate voice between elections. This is the shallowest and weakest conception of democracy.

I do not want to abandon representative democracy. I want to see it balanced by popular sovereignty, especially the variety known as deliberative democracy. By contrast to the adversarial nature of representative democracy, in which politicians try to dominate and vanquish their opponents, deliberative democracy means drawing citizens together to solve problems. It means creating forums in which we listen respectfully to each other, seek to understand each other’s views, change our minds when necessary, and create the rich, informed democratic culture currently missing from national life.

Perhaps the best example is the participatory budgeting programme in the Brazilian city of Porto Alegre. Between 1989 and 2004, citizens were able to decide how the city’s entire investment budget should be spent. The process was designed by government and people working together, and was allowed to evolve as citizens suggested improvements. Some 50,000 people a year participated.

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Instead of being captured by corrupt politicians and local mafias, the people’s decisions ensured that the money went where it was needed most, greatly improving sanitation, clean water, green space, health and education, transforming the lives of the poor. Porto Alegre became the Brazilian state capital with the highest ranking on the human development index. The more people engaged, the wider and deeper their political understanding became. Short-termism was replaced by long-term thinking: essential if we are to confront environmental breakdown.

There are plenty of other ways in which deliberative democracy can change our lives. In Ireland, a citizens’ assembly on abortion law turned an angry debate into a considered one. It tested competing claims and ideas, and led eventually to a referendum. The Better Reykjavík programme allows the citizens of Iceland’s capital to put forward ideas for the city’s improvement, which other people vote on. The 15 most popular ideas every month are passed to the city council to consider. The programme has remodelled Reykjavík in fascinating ways.

Constitutional conventions can be used to draw up principles of government, on which the rest of the population can then vote. Some of the best models are those developed by the Canadian provinces of British Columbia and Ontario. Members of the convention are drawn by lot and informed by experts, field trips and submissions from other citizens. The UK is in urgent need of one.

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But for all the rhetoric about the people’s will, nothing of the kind is on offer in Britain. The so-called citizens’ assembly on climate change proposed by parliament is a cynical caricature of participation. It has a restrictive agenda, a narrow range of advisers and no time for effective deliberation. Digital tools offer massive opportunities for fine-tuning political decisions, but our cod-medieval system – all Black Rods and serjeants at arms – is stuck in the age of the quill pen. The only new form of participation we have been granted this century is an enhanced right to petition parliament, introduced by Tony Blair in 2006. Did it seem radical and innovative? Only until you remember that a similar concession appears to have been made by Edward I in 1275.

The European referendum, that apparently represents the people’s will, was reduced to such a crude choice that no one knows exactly what the majority voted for. Rather than encouraging an informed, nuanced politics, it has made our system even more adversarial, binary and reductive.

I could see the point of Brexit if it meant returning power to the people. But Johnson is as contemptuous of popular sovereignty as he is of parliamentary sovereignty. He seeks sovereignty of a different kind: autocratic control over both parliament and people.

I would love to see Labour placing radical democratic reform at the heart of its manifesto, seeking not to take power but to give it away. I suspect its offer will be limited, until we can build movements big enough to force our governments to let the people speak. Participation in politics is a not a gift. It is our right.

• George Monbiot is a Guardian columnist