It is when politicians make millenarian claims of permanent irreversibility for any policy that you know they and the accompanying project are in trouble. I remember, from my teenage years, Rhodesia’s then prime minister, Ian Smith, unilaterally declaring independence, proclaiming that the new country would last a thousand years; the extravagance of the claim was required because of its very improbability. You knew he was on doomed ground.

Similarly, Boris Johnson’s now infamous leaked dinner remarks declaring that he had no doubt that Britain would leave the EU, which would be “irreversible”. It was a sign that the Brexit cause has its back against the wall – constructing an alternative reality based on faith and ideology in the face of real world facts that refuse to accommodate themselves to Brexiter will. This is the first harbinger of political doom: if you can’t think straight, you regress to claims of irreversibility. The policy that follows will prove unworkable.

Brexiters confront three realities that they can’t and won’t accept, forcing them into ever wilder statements of promise and impossible public negotiating positions. The first is that there is no open sea into which Brexit Britain can sail that offers no constraints on sovereignty, is free of trade-offs and confers only rich possibility. It is fantasy. There are no quick and easy trade deals with the US and China to compensate for the loss of trade with the 27 members of the EU and the 61 countries with which it has deals or deals in the making, constituting together 45% of the world’s countries.

The mathematics don’t add up. In any case, the World Trade Organization, so beloved of Brexiters as their new free trade guardian, is a broken reed. Riven by factions and with no enforcement powers, it is incapable of even adjudicating between the countries waging dangerous trade wars, let alone stopping them. To leave the sanctuary of global EU is to swim with crocodiles.

The second reality is that Britain, an extraordinarily open economy for its size, is dependent on the frictionless trade offered by the single market and the customs union to sustain its prosperity. Every attempt at creating the same effect – from “max fac”, to the tortured compromises on the Irish border, to the Labour party’s no less unworkable proposition of a “shared single market” – necessarily falls short.

Frictionless trade means accepting EU practices, regulations and standards – ie surrendering control, the Brexit red line. Inside the EU, Britain ensured that all but a fraction of the regulations and standards suited it, a wonderful position of having your cake and eating it. Outside, it faces huge expense, loss of control and reduced access to its closest markets. Inward investment has plummeted: car industry investment has halved as companies take stock of the receding market possibilities. Again, madness. Outside the EU, Brexit Britain is going to have to accept EU regulations that are emerging as the global standard – the “Brussels effect”. Only the US and China, with their vast markets, have a chance of challenging these, but US companies in particular know that if they conform to the EU’s gold standard they will conform to lower US ones, so it’s easier to do just that. So will British companies, orbiting around the EU as Johnson fears, but with no voice in determining the standards they follow. It may be stupid and self-defeating, but so is the whole Brexit case.

There is zero appetite beyond the rightwing Brexit bunker for more rank economic failures and social inequities.

Third, and as telling, what fired Brexiters was the chance, outside the EU, of completing the Thatcher revolution. But as the Brexiter transport secretary, Chris Grayling, is forced to take the East Coast mainline into public ownership while damning the privatised industry for neglect of passengers, there is zero appetite beyond the rightwing Brexit bunker for more rank economic failures and social inequities of Thatcherism 2.0.

Last week came two more signs of its receding appeal – the stepping down of Paul Dacre as editor of Daily Mail and his replacement by Geordie Greig, tasked with detoxifying the paper, and an intriguing speech by the environment secretary, Michael Gove, damning contemporary “crony capitalism” for feathering its nest while disregarding its wider social obligations. The Brexit bonfire of EU “red tape” protecting worker rights and the environment, which was going to set the UK economy free – another fantasy – is not going to happen. Instead, outside the EU, or so this line goes, Britain is going to try to be more like Germany and the Scandinavian economies. Again, mad.

Facebook Twitter Pinterest Paul Dacre has been replaced as editor of the Daily Mail by Geordie Greig. Photograph: Dan Kitwood/Getty Images

As a policy, Brexit is beginning to look like the poll tax: attractive as a rightwing pet project but disastrous in practice. Then, the Tory party still had enough political nous to rescue itself, even at the cost of losing its prime minister. Now, as Johnson acknowledges and David Davis’s threatened resignation symbolised, it is at war with itself and the realists are trying to rescue a third-best solution against those in Brexit La-La land.

Theresa May’s impossible mission is to reconcile Jacob Rees-Mogg and Nigel Farage’s red lines on sovereignty, freedom of movement and leaving every EU institution and trade policy, with an economy that requires the opposite. It would be hard enough with a united cabinet and years of negotiating time; within the two years allowed by the article 50 process and Brexit millenarian narcissists it cannot be done.

Occasionally in politics there is the opportunity to do the right thing and secure massive party advantage. If Jeremy Corbyn were to declare that the Labour party wanted to stay in the EU – crucially, only politically sellable with new and aggressive initiatives to identify, control and manage the numbers of immigrants – I feel he would transform his and his party’s standing. In part, he doesn’t because he remains transfixed by the referendum result; in part because he is a Eurosceptic and in part because he sees himself as leading a social movement rather than a political party.

But democracy should never stop – the people can vote again. Brexit is a proved dead end and the point of social protest is not the process of protest Corbyn so reveres, but to change things. Britain is heading towards the rocks. It is time for Labour to step up to the mark.

• Will Hutton is an Observer columnist