The EU is infected by a “populist leprosy”; its fate hangs in the balance; the cracks in the organisation are widening. These are not the ravings of a deluded Brexiter. On the contrary, they are the views of, respectively, the president of France, the chancellor of Germany and the president of the European Commission.

Emmanuel Macron, Angela Merkel and Jean-Claude Juncker were speaking before last week’s EU summit. The agreement reached there on migration allowed the three leaders to claim modest progress. But there is no doubt that internal pressures on the EU are mounting. With populist and nationalist politicians in power in Italy, Poland, Hungary, Austria and Slovenia, it is becoming harder to form an EU consensus. Further rows on migration, reform of the eurozone and the EU budget are all but guaranteed.

External pressures are also mounting. Donald Trump’s hostility to the bloc becomes plainer by the day. Last week the US president tweeted that the EU was “set up to take advantage of the US”, a dramatic departure from America’s traditionally supportive attitude. In a couple of weeks’ time, Mr Trump will hold his first summit with another leader with a considerable animus against the EU: Russia’s Vladimir Putin. The EU’s political leaders have reason to watch that meeting with real apprehension.

If Mr Trump follows through on his threat to levy huge tariffs on European cars, the pressures on EU leaders will only increase. Yet, oddly enough, the Trump administration may be doing the bloc a favour. Just at the time that internal tensions are building among the 28 member states, the US is reminding them of the importance of a collective defence of European interests.

European leaders are intensely aware that America’s EU strategy (as well as China’s and Russia’s) is likely to be an effort to “divide and rule”. With its 28 national governments (soon to be 27) and ponderous governance structure, the EU is a tempting target for such tactics. But, for all their differences, the bloc’s leaders understand the strategic importance of their unity on trade, particularly if a global trade war is indeed in the offing.