Giant butter mountains, wine lakes and an apocryphal EU ban on bendy bananas formed the mythological backdrop to Britain’s 2016 Brexit referendum debacle. Yet while many Vote Leave claims were exaggerated, inaccurate or blatantly untrue, the EU’s capacity for laying itself open to ridicule is undiminished 10 years on. Take the strange case of the whingeing EU commissioners, annoyed that their officially provided electric vehicles cannot manage the time-consuming 280-mile journey between Brussels and Strasbourg without stopping to recharge.

This important issue, first reported by Politico, raises vital questions. Do these highly paid bureaucrats really need chauffeur-driven “company cars”? Surely they could catch a train, or fly, or cycle. EV use is mandatory for road trips. The vehicles are supplied in line with the EU’s Green Deal emissions-cutting policy, which commissioners might be expected to support, not carp about. So why is the commission president, Ursula von der Leyen, allowed a petrol engine? The biggest question of all is why make these tedious Brussels-Strasbourg journeys in the first place?

The answer is the European parliament does not deign to operate like any old common-or-garden parliament. It holds sessions in both cities, as laid down by treaty. Twelve times a year, commissioners, officials and hundreds of MEPs make the trip at a cost to taxpayers of tens of millions of euros. In 2023, a train due to take MEPs to Strasbourg was accidentally diverted to Disneyland, which some unkind people thought only fitting. Yet for all the trouble and expense, France would never allow Strasbourg to be bypassed. National prestige is at stake.

Such EU “gravy train” stories scandalised UK Brexiters but do not appear to faze today’s voters on Europe’s northernmost fringes, where renewed interest and even enthusiasm for the EU is unexpectedly growing. Iceland will hold a national referendum in August on resuming accession negotiations. It signed a security and defence partnership with Brussels in March. In Norway, a longstanding EU hold-out, the main conservative opposition party now wants the country to join the bloc. Faroe Islanders, too, are reportedly having second thoughts about seeking independence from EU member Denmark.

Two common factors are melting cold northern hearts. One is Donald Trump’s pressure campaign on Greenland – sovereign Danish territory that he has threatened to annex “whether they like it or not”. The US president, who also has designs on Canada, Cuba and Panama and recently kidnapped Venezuela’s president, says control of resource-rich Greenland is necessary for US security. This smash-and-grab policy reflects Trump’s belief in imperial US dominion over the western hemisphere – what Russians, in their sphere, used to call the “near abroad”.

Trump’s aggressive iceboat diplomacy has set alarm bells ringing across the far north. After unusually fierce criticism from EU and Nato leaders, Trump, preoccupied by his Iran fiasco, has piped down for now – but he has not given up. After inviting himself to the capital, Nuuk, this month, Jeff Landry, Trump’s “special envoy” (who, bizarrely, is also Republican governor of Louisiana), was bluntly told by prime minister Jens-Frederik Nielsen that Greenland “is not for sale”. Unsurprisingly, US threats have placed Greenlanders’ dreams of independence on ice, driving them closer to Denmark and the EU.

Pointing to a second common factor influencing regional opinion, Þorgerður Katrín Gunnarsdóttir, Iceland’s foreign minister, told the Guardian’s Miranda Bryant this week she was worried covert and malign Russian interference in Reykjavík’s forthcoming EU referendum might assist the “no” campaign and produce Iceland’s own “Brexit moment”. Misinformation and rhetoric taken straight “from the playbook of Nigel Farage and Reform” were potentially distorting the outcome, she warned.

Viewed more broadly, intensifying, destabilising Russian, US and Chinese competition in the strategically important, increasingly accessible Arctic region is concentrating local people’s attention on the benefits of belonging to large, multinational groupings such as the EU. Iceland, like Greenland, has no armed forces of its own and relies on Nato – meaning, principally, the US – for defence. But in the age of Trump, that security umbrella is full of holes, as larger European countries, including Britain, are discovering to their cost.

EU membership, or more specifically, membership renewal, has also become an awkward central issue in the pivotal UK byelection in Makerfield on 18 June, which, coincidentally, is the anniversary of the battle of Waterloo. Keir Starmer wants to reset UK-EU relations. His likely leadership rivals, Andy Burnham, Labour’s candidate in Makerfield, and Wes Streeting, both favour a return to the EU fold, sooner or later. Reform wants the vote to be all about Europe and the government’s “betrayal”. Evelyn Waugh might have called it Brexit revisited, this time without the jokes.

All this interest in joining, rejoining, huddling closer to (or repelling) the EU begs a larger question: is Brussels equal to the geopolitical moment? The twin threats from east and west provide unique incentives to revitalise and reform its venerable, rule-bound, sclerotic institutions. Escalating efforts by Russia, failing in Ukraine, to intimidate and destabilise European states using cyber-attacks, sabotage, assassination, disinformation and quasi-military provocations, such as the recent electronic jamming attack on UK defence secretary John Healey’s RAF plane, were highlighted this week by GCHQ’s surveillance chief, Anne Keast-Butler. “Russia is scaling up its daily hybrid activity against the UK and Europe,” she declared.

EU responses to Trump have been uncoordinated and over-conciliatory, although national leaders such as Germany’s Friedrich Merz have taken a tougher line on Iran. Last year’s US-EU trade deal was a humiliation. On support for Ukraine, Europe has mostly succeeded in maintaining unity in the face of Vladimir Putin’s aggression and Trump’s egregious backsliding, although in practical terms, it typically does too little, too late. As for Ukraine’s membership bid, and enlargement policy in general, the EU’s recent record is poor. Candidate countries are queueing up across the Balkans and eastern Europe. Turkey has been waiting since 1987.

Despite the efforts of France’s president, Emmanuel Macron, the EU is still years away from creating a credible, autonomous “European army”, distinct from US-dominated Nato, and it continues to underachieve in terms of shared weapons manufacturing and procurement. While von der Leyen is adept at keeping numerous plates spinning in the air, she inevitably goes round in circles. Opportunities to strengthen the EU by definitively mending fences with Hungary, post-Viktor Orbán, and with a prodigal UK, are at risk of being missed, obstructed by member states’ perennial budget arguments, national rivalries, lack of political imagination and chronic inertia in Brussels.

Faith among the citizens of Iceland, Greenland and other friends in the north that the EU can help them survive and prosper in a more dangerous world is hopefully not misplaced. Predators such as Putin and Trump, and allied forces of reaction, such as Reform UK, will not wait for Europe if Europe fails to seize the moment. Those whingeing Brussels commissioners should get on their bikes.

• Simon Tisdall is a Guardian foreign affairs commentator