Maybe the European Union is God’s way of teaching the British about Belgium. Specifically, it is a mechanism that forces UK politicians to confront the idea that Belgium matters. And not just Belgium but countries like it – the small countries.

This concept doesn’t come naturally to a nation that is neurotically worried about its greatness. Naming famous Belgians is a parlour game for British foreign secretaries. Cultivating small-state alliances feels like something less ambitious countries do. The UK struggles to see itself in perspective because it is richer and more powerful than most countries, yet so much less influential than it used to be.

We are not alone in suffering from post-imperial angst, but we have tied ourselves in uniquely existential knots where relations with our European neighbours are concerned. Theresa May understands the deep cultural and psychological attraction of Brexit as a great unpicking – a disentanglement from continental ties, the benefits of which feel obscure to much of the public.

Therein lies the emotional cleverness of the prime minister’s formulation of a “clean Brexit”, as laid out in her speech on Tuesday. Pro-Europeans probe the agonising detail of the negotiations to come without recruiting any more of the public to share their pain. If anything, the balance of opinion is swinging the other way. The prime minister’s message was tailored to the large segment of voters, including many ex-remainers, who see the big in/out question as settled and say they want the job done without any more palaver.

The effectiveness of May’s account of future relations with the EU – no “partial membership”, no messy overlaps with the past – is its simplicity. Her Europhile critics want to talk only about complexity, which is the least catchy tune in politics. May paints Britain with the crispness of its outline restored, its place in the world made clearer by the erasure of all those fiddly lines that connect London to Brussels and then to Paris, Berlin, Ljubljana, Tallinn and the rest. She offers liberation from the need to care about Belgians.

That obligation endures whether the prime minister wants it or not. Small states will have a say in the divorce contract terms that Britain signs with the EU. Their voice will be heard in the negotiations and in chambers where the deal must be ratified. It was opposition in Belgium’s Wallonian regional parliament that nearly scuppered a Canada-EU free trade agreement last year.

No less important than pragmatic attention to small-state sensibilities is the strategic and moral duty that Britain owes to lesser powers. The EU has historically been good at inflating the influence of minor capitals, to the frustration of major ones. It has also allowed the most powerful economies – Germany, France and the UK – to throw their weight around, to the annoyance of lesser players. This voluntary national surrender of autonomy in some dimensions for greater influence in others is the essence of the European project, and it mystifies the kind of politician who wants international relations to be a league table of countries, with an obvious champion at the top.

When, earlier this week, Donald Trump described the EU dismissively as “a vehicle for Germany” likely to lose more members after Brexit, he was aggravating diplomatic vandalism with historical ignorance. The apparatus of European integration first came into existence, and has been sustained in large part, by German atonement for its 20th-century crimes, expressed as willingness to subordinate a narrowly defined national interest for wider continental cooperation.

But Trump struggles with the concept of mutual arrangements that guarantee stability without yielding a fist-pumping victory or cash payout to one party. He craves the firm smack of a deal. He appears to find the idea of big countries lending power to smaller ones for the sake of anything so sissy as “shared values” contemptible. He sees Nato as a European tax on the US military.

May's speech imagined a place where Britain has freedom to choose its friends and decide its status in the world

It is one of the ways in which his instincts and those of Vladimir Putin are aligned. The Russian president also has no interest in a system of international relations based on rules and protocol. For Putin, the EU has always been an obstacle to the pursuit of a divide-and-rule strategy within the former Soviet sphere of influence in the old Eastern bloc. He and Trump would both prefer a Europe of disparate and disorganised nation states, all potential clients of Washington and Moscow, without an organising principle of their own.

This is not May’s vision. In her speech she emphasised a hope that the EU succeed post-Brexit, and underlined her belief that the union should not unravel. That such a wish even has to be expressed testifies to a world in alarming flux.

The US is about to acquire a president who is relaxed about the dissolution of essential pillars of European security, when not actively undermining them. And this is the president whose offer of a trade deal is meant to give Britain confidence that Brexit will work. Given Trump’s known views on trade and the aggressive protectionists whose company he keeps, it is safe to presume that the non-negotiable terms of that deal will be total vassalage to US corporate interests. It will require a surrender of economic sovereignty every bit as great as that involved in EU membership, with none of the accompanying diplomatic clout.

May’s speech on Tuesday was meant to be a beacon illuminating Britain’s future outside the EU. But, coming days before Trump’s inauguration, it should be read also as an unwitting requiem for the global order that is passing away. It imagined a place where the contours of power are neatly defined and stable, where Britain has freedom to choose its friends and decide its status in the world. Viewed from Trump Tower, Britain sits in the bottom half of the first division of world players: a leading G7 economy, a nuclear-armed security council member, but not a superpower. Our interests matter, but probably not that much more than Belgian interests currently matter in Whitehall.

It’s a question of perspective. For decades Britain has struggled to get a comfortable sense of its scale relative to the rest of the world. We are about to find out how big – or small – we really are.