This might not feel like the moment to go on about Brexit, but Brexit goes on whether we are feeling it or not. When people are worried about surviving April, December’s deadline for EU trade talks seems a long way off. Covid-19 may have eclipsed older problems, but they will not solve themselves in its shadow.

The disease has halted negotiations and infected the lead negotiators. All Whitehall capacity is being spent on the immediate crisis. Boris Johnson has no time for Brexit. If he did, he might want to practise some social distancing from the idea.

Suppose for a moment that Britain had not already committed to quitting the single market. Then imagine the government choosing the peak of a pandemic to plan new obstructions for goods flowing between the UK and Europe. Picture Rishi Sunak, wunderkind chancellor, explaining why supply chains must be disrupted and friction added at Channel ports. Ponder ministers selling the idea of a customs border between mainland Britain and Northern Ireland – sand in the wheels of recovery, plus salt in the wounds of history. Pitched that way, as a post-viral convalescence strategy, the UK’s Brexit trajectory is absurd. Johnson’s best-case scenario – a “Canada-style” deal – promises only shock to a debilitated system.

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Even before coronavirus, the December deadline looked fanciful. Transitional arrangements can be extended if a request is made in Brussels by the end of June but Downing Street denies thinking of such a thing. The official line stresses that the current timetable is enshrined in law, as if to imply that it cannot be changed.

It can, but only with parliament’s permission, and the prime minister is in no hurry to ask his MPs. Civil servants and some senior Tories think he has no choice, but they see logic in leaving it to the last minute. The crisis will get worse before it eases, and the further Johnson marches his party down this gruelling road, the more of its unwieldy ideological baggage gets discarded. A few more weeks of lockdown and Brexit hardliners might be persuaded to rubber-stamp a second year of transition, given that the first one will be lost to sickness.

Covid-19 has already ravaged conservative orthodoxy, provoking economic intervention on a scale unimagined by any chancellor in recent history. Fiscal discipline is gone, while the new state bossiness about private behaviour makes libertarian Tories squirm. Euroscepticism has not yet been compromised in the same way, but that doesn’t mean it is immune.

There are early symptoms of discomfort in the government’s confused response to a joint European tender for emergency medical equipment. No 10 said it had not taken part because of Brexit, then changed its story. They claim an email invitation had been missed. But officials had known of the scheme for months. By some combination of arrogance and incompetence the government excluded itself from one piece of European cooperation that no one could reasonably denounce as a compromise on sovereignty.

That mistake doesn’t yet carry a political penalty. Details of what the EU actually does has never much excited public opinion, except when it can be caricatured as an affront to cultural autonomy. But the urge to cut every fibre of every thread that binds the UK to Europe is also a minority compulsion. Johnson’s electoral mandate was to get Brexit done, mainly so that sweaty European debates might be relegated back to their pre-referendum position on the political fringes. If the prime minister now decided that the small print needed amendment I doubt there would be uproar. If there is one person in Britain capable of serving hard Brexiteers something softer while claiming the taste is the same, Johnson is that man.

In the longer term, events have a way of proving everyone right in their own imagination. Pro-Europeans will see the pandemic as confirmation that modern threats know no borders, and that cooperation on a continental scale is the inevitable solution. Eurosceptics will point to the primacy of national responses in every country to argue that the plot for a federal superstate goes against nature’s grain. Each side will find evidence to support their view. The crisis offers examples of cross-border solidarity and nationalist self-isolation.

It has demonstrated the logic of continental cooperation and probed continental fault lines. There is renewed tension within the eurozone because German and Dutch taxpayers don’t like underwriting Italian debts. There is dismay at Vikor Orbán using the cloak of emergency powers to suffocate what democratic spirit is left in Hungary. The virus will also be a shared trauma that might, as in the past, cultivate the sense of common destiny that underpins collaborative European politics.

EU structures will evolve through Covid-19, as will the character of the European project. Britain will have to define its relationships in this new context, although plenty of people in Westminster would rather resume the old debate or pretend there is no debate to be had – that campaign rhetoric from 2019 answers questions unasked before 2020.

The thing called “Europe” that has dominated British politics in recent years is a creature of the Eurosceptic imagination, with only cartoon resemblance to the real EU, animated by exaggeration of powers held in Brussels and paranoia about the way they are wielded.

Now that the nation faces a truly frightening menace it should be obvious that EU membership never belonged in that category. The downsides were too banal to justify the bellicose frenzy against it. The reasons people gave for separation have not gone away, but it gets harder to mould that cause as the stuff of national glory. Escaping continental regulations for processed fish is not in the same bracket as Agincourt and Dunkirk.

Eurosceptics will claim vindication if coronavirus plunges the EU into an existential crisis, but history might also judge them harshly. They waged a generation-long battle against imaginary threats, claiming victory on the eve of meeting a real one. Coronavirus has not just bumped Brexit down the political agenda, it makes the whole project look parochial and self-indulgent. Britain’s EU membership expired on 31 January, but the doctrine that cast Europe as a national affliction should be buried alongside it.

• Rafael Behr is a Guardian columnist