EU officials in Brussels have a habit of telling us Brits that we don’t get it: Brexit is not the biggest show in town. After all, the EU has more important things to worry about – migration; illiberal nationalists in Hungary and Poland; eurozone reforms; Donald Trump – and everyone desperately wants to move on from Brexit.

They certainly have something much bigger to worry about now: the political turmoil in Italy could easily turn into an existential crisis for the euro and the EU. Sergio Mattarella, the Italian president, blocked the appointment as finance minister of Paolo Savona, a Eurosceptic who wants Italy to leave the euro. As a result, a coalition between the two populist parties who topped the poll in March’s election – the anti-establishment Five Star Movement and the Eurosceptic far-right League – is on hold and a technocrat, Carlo Cottarelli, has been asked to head Italy’s 66th government since the Second World War (yes, an average of almost one a year).

The president probably felt he was damned if he did and damned if he didn’t veto Savona. He might have averted an immediate crisis. But he might have walked into a trap laid by Matteo Salvini, the League’s leader, who then refused to nominate a compromise candidate for finance minister, probably in the hope that the ensuing chaos would force another election.

Although there is speculation today about fresh talks on a populist coalition, an election could come as early as July and in effect become a referendum on the euro and the EU. With the two populist parties rising in the opinion polls, no wonder the EU is fretting about Italy, a founder member which will be its third largest economy when the UK departs.

Inevitably, Eurosceptics in Britain have seized on the Italian president’s move as another wicked plot by Brussels to deny the democratic will of the people. They spy such plots round every corner. Usually they don’t exist, but the EU has not helped itself on this occasion. Gunther Oettinger, its budget commissioner, warned: “The markets will teach the Italians to vote for the right thing.” Although he later apologised, the damage was done, and will surely be exploited in the next Italian election.

Events in Italy could have a knock-on effect on the Brexit negotiations. Although EU figures admitted the bloc needed to learn lessons after the UK’s 2016 referendum, the instinct of some will be to punish the UK even harder to keep their cherished project intact.

British officials sense that mindset in the EU’s attempt to freeze the UK out of its Galileo satellite navigation system and future EU defence contracts because it will be merely a “third country” like any other. Hopefully, wiser heads will prevail: the EU, like the UK, needs a good exit agreement and trade deal.

George Soros donates to anti-brexit campaign

Five Star has pledged that, as part of the next Italian government, it would stop the EU’s “punishment” of the UK since Brexit is also about “respect for democracy”. But Theresa May cannot rely on such promises. She would be wise to distance herself from the Italian populists; it would not serve Britain’s interests for Brussels to view Brexit as part of a plan to destroy the EU. In any case, Five Star may benefit less from another election than League, which might revive its right-wing alliance with Forza Italia, whose leader Silvio Berlusconi, the former prime minister and a relative moderate these days, is free to stand for public office after a ban for tax fraud was lifted.

To survive and prosper, the EU will need to forget the federalists’ dreams of ever closer union and become a more flexible, multitrack club. Although the UK won an opt-out from the single currency, it was not enough when migration – also a driver of the populists’ advance in Italy – came to the fore.

Arguably, if David Cameron had secured something on free movement, Brexit might not have happened. As George Soros, the financier and backer of the anti-Brexit Best for Britain group, put it yesterday: “The EU needs to reinvent itself.”

Brexiteers are enjoying the turmoil in Italy. They can’t wait to dance on the euro’s grave, hoping its demise might lead to the EU’s collapse. We have heard this tune before. Remember the Greek crisis? The last time I checked, Greece was still in the eurozone.

As May has acknowledged, it is in the UK’s economic interests for the EU to succeed. Whatever Brexit’s final shape, the EU will remain our biggest trading partner for years, perhaps forever. The wobble over Italy on financial markets around the world is a reminder of how economies are interdependent.