In Britain’s unfolding constitutional crisis, Theresa May is living with the consequences of a series of decisions calculated to keep hold of the keys to No 10. By establishing “red lines” she knew were unrealistic, the prime minister presented herself as the custodian of the interests of the 52%, promising to deliver on the outlandish pledges made by the leave campaign. This was a naked political calculation: the mantra “Brexit means Brexit” would boost her polling and an early election would then provide the large majority she needed to make the U-turn ahead.

We all know how well that plan panned out.

There is, however, a lesson in May’s political-cum-personal tragedy for politicians of all parties: the Brexit crisis will punish those who put power before principle.

At the root of the problem Brexit poses to our democracy is a simple contradiction. On the one hand, a “hard” break with European institutions means a high level of economic dislocation. The electorate would punish any government that carried out such an exit at the ballot box, cruelly blaming them despite their protestations to be implementing the “will of the people”. On the other hand, a “soft” exit would be less damaging economically, but harmful politically. As a new report argues, far from “taking back control”, Britain would be forced to adopt rules that it ultimately has little say over.

This problem of a loss of sovereignty is particularly acute in the so-called Norway-plus model. With May’s deal looking unlikely to pass through parliament, some MPs have promoted this as an alternative. Tory backbencher Nick Boles has launched a low-budget website calling for it, while Labour moderate Stephen Kinnock has claimed there is a “strong and growing cross-party consensus” for a Norway-plus deal.

So what exactly is Norway-plus?

Norway is a member of the single market through the European Economic Area (EEA), which acts as an outer periphery of the European Union for countries that are either not seeking, or transitioning towards, full membership. Norway has to accept EU single market rules in a range of areas, making up some 6,000 legal acts. It makes payments into the EU budget, but without any representation in the European parliament, commission or council.

Instead, the Norwegian government acts as a kind of state-lobbyist in Brussels. It also tries to influence the commission through the EEA’s joint committee, where it has to accept new rules or risk losing access to the EU market. As the Norwegian prime minister, Erna Solberg, has argued the model would be very “difficult for Britain, because … Brussels will decide without the Brits being able to participate in the decision-making.” Meanwhile, senior Norwegian politicians are turning against any plan for the UK to join its trading agreement with the EU.

A Norway-style deal on its own would also not work for Britain. There are customs checks at the land border between the EU and Norway, because the country is not part of the customs union. This is unacceptable for the UK and EU due to the need to maintain an open land border with Ireland. Norway-plus is designed to solve this problem, where the “plus” refers to entering a permanent customs union with the EU. So not only would the UK adopt EU single market regulations, it would also have to accept trade and tariff rules.

‘Negotiations over a Norway-style agreement would be tough going for Britain. The principle obstacle would be fisheries policy, which is not covered by the EEA agreement.’ Photograph: Jeff J Mitchell/Getty Images

Although sometimes misleadingly promoted as an off-the-shelf option, negotiations over a Norway-style agreement would be tough going for Britain. The principle obstacle would be fisheries policy, which is not covered by the EEA agreement. With France and Spain committed to maintaining access to UK fishing waters, a government seeking an EEA-like alternative would likely have to adopt an EEA-plus-plus policy, where the second plus refers to the European common fisheries policy.

All this being the case, if Brexit is looked at purely from a business perspective, the EEA option has merits. Having a democratic say is less important if you accept the status quo. For many Labour moderates and Conservative politicians this is the case.

The Labour leadership, however, has a transformative agenda for Britain and Europe. It seeks far-reaching reform of European and global capitalism. Losing democratic representation in EU structures would be potentially crippling to this project.

The tragedy of Brexit is that all routes out of the EU lead in this direction. May’s deal, too, would see the UK entering the single market for goods, accepting its rules, and so on, while lobbying the EU through a joint committee similar to the EEA structure.

To continue with Brexit means recognising that it entails a loss of democratic control over many of the big, global issues affecting the daily lives of UK citizens. For Labour’s left this is clearly unacceptable. A radical vision of social change requires fundamentally unleashing popular democracy, not curtailing it.

With the scope for triangulation becoming tighter, and a constitutional crisis in Britain underway, Labour should look these realities squarely in the face and offer a way out. The case for staying in the EU is stronger than ever.

• Luke Cooper is a senior lecturer in international politics at Anglia Ruskin University and a convenor of the Another Europe Is Possible campaign