Sure enough, world leaders have rushed to accommodate themselves to the new dispensation. The last thing they want, what with the euro crisis still smouldering, is a protracted row with the UK. It is in everyone’s interest to reach a deal as amicably as possible.

Angela Merkel, the German Chancellor, says it’s important to be “calm and composed” while seeking to negotiate “close future relations” with Britain. The Polish foreign minister, Witold Waszczykowski, says the vote showed “disillusionment with European integration”.

The President of the European parliament, Martin Schulz, an old-style federalist who loathes Euroscepticism, spoke frankly about his worry that there would be “a chain reaction”.

Frankly you can see his point. Britons are not unique in their dislike of Brussels. The EU’s in-house polling agency, Eurobarometer, records comparable levels of distrust in Spain, Germany, France and Sweden – and much higher levels in Greece.

Unlike the populist politicians in some continental countries, British Eurosceptics tend to be internationalist and free-trading. No politician here is remotely comparable to, say, Marine Le Pen, currently leading the polls in France, whose dislike of Brussels blends with her dislike of America, capitalism and liberalism.

The leaders of our Leave campaign are, from the EU’s perspective, as benign as a Eurosceptic can be. Michael Gove is steeped in European culture. His talented wife is, more or less, Italian. Gove has always supported deeper trade and co-operation with Europe; he just wants the right to hire and fire our own law-makers.

Boris Johnson is an old boy of the European School in Brussels where Eurocrats educate their Eurobrats. He speaks French and Italian, sings in German and, like Gove, wants Britain to remain engaged with every continent including Europe. Both men argued for Brexit on grounds that diversity and democracy were European values.

Behind Herr Schulz’s worry about a “chain reaction” is a well-founded concern. The next Eurosceptic insurgency is unlikely to be as mild as Britain’s. It might come from France’s National Front, or from the anti-immigrant Alternative for Germany, or from nativist parties in Eastern Europe. It might take the form of a radical Left movement, such as Spain’s Podemos or Italy’s Five Star Movement.

The real question in Brussels is how to handle Brexit so as to soothe rather than inflame tensions on the Continent. Provoking a fight would risk rekindling the crisis in the Eurozone, possibly spreading it to Italy or France.

No, the obvious course is to do what that old federalist warhorse Jacques Delors proposed right at the outset, namely to offer Britain a “privileged partnership”, based on a common market rather than common political institutions. Many other Euro-integrationists have taken up this theme, including Valery Giscard d’Estaing, the author of the European Constitution, and Guy Verhofstadt, the former Belgiam prime minister who now leads the Liberal MEPs, and who calls it “associate membership”.

The outlines of the scheme are clear enough. Britain would end the supremacy of EU law over national statutes and withdraw, in a phased and measured way, from several of the non-economic parts of membership, including aspects of foreign affairs, criminal justice, farming, fishing and citizenship. But it would leave in place bulk of the EU’s economic arrangements.

Obviously, details matter. Brussels takes a very broad view of what count as economic arrangements: all its environmental rules, for example, are introduced as single market measures. The question of how to arbitrate trade issues would be critical: would a new tribunal be created, as with EFTA, or could the economic and non-economic aspects of the EU’s existing institutions be separated?

Plus, obviously, there is sensitive issue of migration. While the UK could disapply EU citizenship, and thus regain the power to deport undesirables and refuse entry to the economically unproductive, it might have to retain free movement of labour – that is, the pre-Maastricht system where EU nationals with a specific job offer have the right to settle in each other’s states.

While there will be bargaining on all these issues, none should be impossible to resolve. Both sides have an incentive to settle.

Although Britain now has a mandate to leave, we need to remember that 48 per cent of our people, including majorities in Scotland and Northern Ireland, voted to stay. We should, in short, move slowly, and by consent.

The rest of the EU, for its part, has every reason to reach a deal as smoothly as possible. Offering Britain a form of semi-detached association, which others might then copy, is the surest way to kill off populism on the continent.

If only David Cameron had sought such a deal in the first place.