Brexit is not just one negotiation between two sides. At its heart is the dialogue between the EU and Theresa May’s government, but that process has become increasingly detached from the negotiation that Mrs May conducts with her cabinet, her party, and parliament. The concept of Brexit being presented to British audiences now bears hardly any relation at all to the concept as it is grasped in Brussels.

This disparity is extremely dangerous. For weeks, Mrs May has been bogged down in debate about alternatives to a customs union, as if that is the thing on which a good deal depends. Viewed from Brussels, this looks like refusal to engage with underlying issues, and dereliction of duty to explain to voters what the true choices entail.

The customs union row is a proxy for the question of how far the UK intends to diverge from EU standards and regulations. That issue isn’t addressed directly for two reasons. First, it exposes an ideological schism in the Conservative party. Second, the “joint report” ending the first phase of negotiations in December includes provisions for an invisible Irish border that settle the matter in favour of zero divergence. But Mrs May doesn’t dare say so. The UK government has already signed something in Brussels that requires a soft Brexit and the Tories are performing a pantomime debate behind red lines that require a much harder Brexit. It is an act of monstrous collective irresponsibility.

So what is the real negotiation? In essence, it is about the extent to which the UK can replicate the existing regulatory regime while allowing the prime minister to assert that some “control” has been recovered. In terms of what is most urgent to leave voters, that means immigration control. So the least ruinous deal that might win public consent is an association agreement with the EU. Its potential outline was described this week by Ivan Rogers, the UK’s former ambassador to Brussels: “Quasi single market membership, paying something for it, living under ECJ jurisprudence and jurisdiction in goods, but dis-applying … free movement of people.”

That would be painful for hard Brexiters but also for the EU, since the four freedoms have been said countless times to be indivisible. The prohibition on “cherry-picking” could not have been made clearer. On this point, it is in Brussels that uncomfortable truths must be aired. The European project is imperilled by domestic turmoil in many member states. The formation of a populist-nationalist government in Italy is the latest manifestation of these trends. The Brexit vote expressed peculiarities of British Euroscepticism, but its political and cultural causes were not unique.

After the referendum, Brussels was shaken by fear of contagion. The need for Brexit to fail and be seen to fail seemed imperative. That is no longer the issue. The impossibility of leaving the EU on terms superior to membership has been demonstrated. The new imperative is to show generosity and flexibility to a valued and valuable “third country”. The EU’s big power brokers – France, Germany and the commission – should be imagining alternative models to full membership that might incentivise closer association for non-members, in the western Balkans, for example. Brussels will never be grateful to Britain for creating the Brexit mess, but that doesn’t mean opportunities can’t be salvaged.

The UK government has failed in its duty to level with the public about the scale of compromise and costs involved in Brexit, as indeed has the Labour party. The prime minister is running out of time to realign a delusional domestic debate with international reality. But she has allowed the two spheres to drift so far apart, it is hard to reunite them without triggering a hugely destructive political crisis. Such a combustion would be bad for the rest of Europe, too. Mrs May needs help from Brussels. She cannot unilaterally devise a new, highly integrated model of close partnership. Far from fearing such a partnership as a dangerous precedent, the rest of the EU should welcome it as a sign that their alliance is both more resilient and more flexible than it has so far looked to many ordinary European citizens.