While various prominent figures in Brussels occupied themselves with threatening Brexiteers with eternal damnation this week, they might perhaps have spent their time more productively somewhat closer to home. No doubt Donald Tusk and Guy Verhofstadt dislike the EU losing one of its largest members, but the union has other problems with the relationship between its remaining members.

Only yesterday the simmering tension between Italy and France boiled over, with Paris taking the extraordinary step of withdrawing its ambassador from Rome for the first time since the Second World War.

The spark was a visit by the Italian Deputy Prime Minister to meet some of the Yellow Vest protesters who have rioted against the Macron government in recent months. That meeting was an obvious provocation, and is rightly seen by the French government as an insult to its legitimacy by an outside power.

It didn’t come out of the blue, though. Ideologically, Emmanuel Macron and Matteo Salvini are cut from very different cloth, and their potential to clash is further heightened by the fact that each has eagerly pursued a strategy of defining himself among his domestic supporters by criticising the other. Last June, when Macron described populism as a form of political “leprosy”, Salvini derided the French President as a “chatterbox” who liked to “preach” to European leaders who actually got things done.

The format of the Italian governing coalition also lends itself to a bit of one-upmanship in the game of publicly insulting Macron, as neither party wants to look weaker than its partner. In January, the Deputy Prime Minister – from the 5 Star Movement – accused France of contributing to illegal migration from Africa by a continued policy of imperialism. Salvini then upped the ante by openly calling for French voters to “get rid of a terrible president” – meddling in the domestic politics of an ally to a degree that would be unthinkable in ordinary times. Not to be outdone, his coalition partner has now held this meeting with the gilets jaunes.

Both are playing to a home crowd, quite openly with the goal of outdoing their coalition partner in the forthcoming European elections. While the Italian coalition between Salvini’s nationalist Lega and the anti-establishment hotch-potch which makes up 5 Star has held together far better than most observer (and indeed many members of both parties) expected, that doesn’t mean they have stopped viewing one another as rivals, or dreaming of governing alone. Macron – preachy, smug, and responsible for refusing to admit migrants across the French border while expecting Italy to accept those who come across the Mediterranean – is the punchbag that they now use to display their strength.

It might be a primarily domestic performance, but the effects have been international. France is fuming, and a breakdown in diplomatic relations between two major European nations is a remarkable and rare sight. British Eurosceptics habitually look out for signs of rupture and division within the EU and are prone to declare “Aha, now the wheels are starting to come off.” But is that really the case?

The EU obviously has persistent problems. The eye-watering scale of youth unemployment in the south is well-known. Italy, Austria, Hungary and Poland are now governed by parties which are far from the tastes of the Brussels establishment. Long-established parties of the integrationist mainstream have been swept away in tumultuous elections in several member states. A poll in France earlier this week put support for leaving the EU at 40 per cent – a startlingly high number which would may well cause a cold sweat in various offices in Strasbourg.

However, we Brits should resist the temptation to assume dissent – even explicitly Eurosceptic dissent – across the EU takes the same format, or comes from the same tradition, as Euroscepticism in the UK.

For historical, political and economic reasons, actually wanting to escape or dismantle the EU and its institutions is less popular on the Continent than here. Consider that even in Italy, where a large chunk of the younger generation have had their economic prospects sacrificed on the altar of monetary union, only 25 per cent of people want to leave the Euro, never mind the European Union. Marine Le Pen, supposedly unafraid to court controversy, rowed back from considering Frexit once she got into the final two for the French presidency. Even Yianis Varoufakis, an eye-witness to the willingness of the EU to trample people and countries in the pursuit of its political project, always shied away from advocating an end to membership.

That might change (as Fraser Nelson points out, perhaps the presence of a successful former member might have that effect in time) but ever closer union has so far persisted as an idea, despite a severe buffeting from some pretty horrendous storms of its own making, and it isn’t dead yet.

And yet these tensions between France and Italy (and between Warsaw and Brussels, and Hungary and almost everybody) are real, painful and intensifying. They shouldn’t be misinterpreted or over-interpreted, but equally they can’t simply be ignored or wished away. In reality, what we’re seeing is an attempt not to break up the EU by people like Salvini and Orban, but an attempt to bend it towards their way of thinking and away from that of so-called centrists like Macron.

They know that, at the moment, those wielding power in Brussels are generally in agreement with their opponents, so most of their speeches and actions are pitched against the sensibilities of the EU institutions. But later this year they will be able to appoint their own people to a new Commission, and they will gain a voice at the heart of the EU. When that happens, I wonder if supporters of the current Brussels establishment will be quite so keen on the unaccountable, centralised structures which they built on the assumption that they would run them forever.