The secret history of modern Britain is made in obscure corners between men and women taken seriously by no one but themselves. A good time to begin it would be in the winter of 2013/14 when the Institute of Economic Affairs, a rightist outfit that won’t reveal where its money comes from, offered a €100,000 prize to whoever could devise a means of leaving the European Union.

The reason why politicians are now stumbling towards disaster like prisoners marching to the scaffold ought to have been clear from that moment. Obviously, Britain can leave the EU, but only if it is willing to pay an extortionate price. Yet first the institute’s judges, led by Nigel Lawson and Gisela Stuart, then the Leave campaigns of Boris Johnson, Nigel Farage and Dominic Cummings and, finally, Theresa May and Jeremy Corbyn, who even now cannot speak plainly, have refused to acknowledge the harsh truth.

As if to anticipate their failings, the winning entry came from a minor functionary in the British embassy in Manila by the name of Iain Mansfield. He brushed away the difficulties of leaving the EU and offered us our first helping of unicorn cake. Britain, he declared, could enjoy the free movement of capital and goods in the single market, he announced, but stop the free movement of labour.

His triumph marked an ominous moment. Until 2013, even rightwing politicians accepted that they could not have the best of all possible worlds. Britain was tied into an integrated European economy. No government could wrench it away in a couple of years. Britain would have to stay in the customs union, as Liam Fox said in 2012. The most significant thinker in the Brexit movement went further. Richard North, the advocate of “Flexcit”, warned that, as a sudden departure would wreck people’s lives, Britain would have to be like Norway and stay in the single market, “at least in the medium term”, as it dedicated many years, maybe more than a decade, to flexible negotiations about a future arrangement.

Rationally, a flexible approach made sense. But by the winter of 2013 the market for rational politics was faltering. North described how Lawson and his fellow judges excluded from the shortlist entries that said the only way to leave the EU was to follow the Norwegian example. Until that point, he had had regular meetings with Arron Banks, Owen Patterson and Cummings. “But something then happened – I don’t know what. Cummings went dark on me and I was ‘no platformed’.”

Electorally, allowing millions to believe that the impossible was possible was perfect post-rational politics

You don’t need to be a detective to work out why the darkness fell. How could the Brexit campaign inspire nationalist passions, how could Fox, Lawson, Johnson, Farage and Banks inspire even themselves, if they were to say that the only rational way to leave the EU was to carry on paying money, accepting freedom of movement and receiving laws that Britain had no say in making, while an orderly retreat was organised? Who would vote for that? What would be the point of leaving at all?

Better to take the road to Narnia and promise everything while committing to nothing. After the prize was awarded to a political fantasy, Cummings gave fair warning of what was coming next. Writing in 2015, he admitted that the campaign would offer no exit plan: hard Brexit, soft Brexit or any Brexit in between. “There is much to be gained from swerving the whole issue,” he explained. Opponents of the EU “have been divided for years”. In any case, “the sheer complexity of leaving would involve endless questions of detail that cannot be answered”.

An honourable man, and an honourable political movement, would have found these excellent reasons to think again. Not Cummings and not the Brexit movement. Intellectually, their Brexit was an empty idea. But electorally, allowing millions to believe that the impossible was possible was perfect post-rational politics. As Roland Smith of the Adam Smith Institute, another rightwing thinktank, said last week, the “dirty secret” of the Leave campaign was that it “didn’t have a well-formed idea of how to leave the EU or indeed whether any alternative was really palatable”.

It is easy to portray Cummings, Johnson and Farage as grand villains. Indeed, if we crash out with no deal, we will be hard pressed to find so much misery brought to so many by so few. But the Cameron government, every MP who voted for the referendum, the supposedly ferocious interviewers at the BBC and hard-nosed journalists in the press let them get away with it. None insisted that the voters be told what form of Brexit they were voting for.

As a point of contrast, consider that in 2018 Ireland discussed removing its constitutional ban on abortion. There was an exhaustive debate at a citizens’ assembly on the proposed measures and the government published a policy paper outlining in what circumstances abortion would be legal if the reform were approved in a referendum, so that no one could argue about the result. As a matter of deliberate policy by Brexit’s supporters, and as a consequence of unforgivable negligence by politicians and journalists, Britain’s referendum offered no such clarity.

I hope you can now see the consequences of obscure arguments in political backwaters. Supporters of a “people’s vote” are met with the superficially plausible objection: “But we’ve already had a referendum.” Supporters of May’s deal and the “Norway option” face the objection that the Leave campaign never told them that we would have to accept EU rules once we left. Finally, for the supporters of a hard Brexit and the millions who risk their futures by believing them, crashing out and crying “to hell with it” are the logical consequences of the illogical retreat from reason they began in 2013.

For good or ill, you can guarantee that the arguments that affect us most are the ones that never make it on to evening news. In the case of Brexit Britain, it’s all ill.

• Nick Cohen is an Observer columnist