Five months ago, Donald Trump’s national security adviser HR McMaster penned a column attempting to persuade the world that “America first” did not mean “America alone”. Last week Trump took two decisions that landed the US in a strikingly lonely position: he pulled his country out of Unesco, and took a massive swipe at the 2015 Iran nuclear deal.

The two moves were very different, but both demonstrated utter disdain for the mechanisms and principles of multilateralism, as enshrined in the UN-based international order. Unesco was created to promote culture and education as a vehicle for peace. The Iran accord was painstakingly negotiated by Trump’s predecessor, along with America’s allies Russia and China, to thwart the danger of all-out war across the Middle East and possibly beyond. Importantly, it was unanimously endorsed by UN resolution 2231. That kind of consensus does not come easily – and now it is being wrecked.

Play Video 1:16 Unesco expresses deep regret at US decision to leave organisation – video

Trump’s decisions gave their full meaning to key sentences in the McMaster article, and offered a clear illustration of this administration’s foreign policy outlook. “The world is not a ‘global community’ but an arena where nations, non-governmental actors and businesses engage and compete for advantage,” said that text, adding: “Rather than deny this elemental nature of international affairs, we embrace it.”

So here we all are, thrown into the “arena”. Multilateralism seems to be dying before our eyes. Europe cannot, and will not, be immune. For one thing, recent elections in Austria have shown populism is still at work, tearing at the fabric of EU values. If anything, this will only add to the difficulties already encountered by those who dream of transforming Europe into “the leader of the free world” – to quote Emmanuel Macron, the continent’s current poster child for liberal democracy.

It’s true that other US presidents have lashed out at Unesco in the past; the organisation is not exactly flawless. But no one in the Oval Office before Trump has ever so openly and ideologically run a bulldozer into US-built, post-1945 institutions. Trump had laid it out in his speech at the UN general assembly last month. “The best vehicle for elevating the human condition,” he said, “is the nation state.” Not international cooperation, not global regulation, and certainly not universal values.

With that, the US has now bluntly demonstrated that it is ready to go it alone. In the case of the Iran deal, the consequences for international security are potentially immense, and could unravel quickly. One US senator may not have been exaggerating when he warned that Trump risked putting his country “on the path to world war three”. Trump has refrained from instantly tearing up the nuclear agreement, but he’s put conditions on its survival that Congress and US allies alike will now struggle to address; and he has threatened to deliver a final blow if they don’t comply.

Think about what a war over Iran’s nuclear programme would do: Trump’s policies have put back on the table

To understand the scale of what is happening, remember how intensely Obama wanted to achieve this UN-endorsed 2015 deal with Iran, and how convinced he was that a price worth paying was inaction in Syria against the Assad regime, despite the massacres. Assad is Iran’s protege. Civilians were slaughtered by a dictator’s army. Radicalisation grew. For Europe, the outcome was a massive refugee phenomenon as well as terrorism – which upended the continent’s politics and contributed to Brexit.

Now think about what a war over Iran’s nuclear programme would do to the Middle East and the wider world: it’s a scenario Trump’s reckless policies have now put back on the table. To be sure, multilateralism has hardly been in good shape in recent years. Focusing solely on Trump-related risks makes us forget about how other powers and leaders have already chipped away at a global order designed to prevent conflict and human rights violations. Need one mention George W Bush and Tony Blair’s 2003 decision to invade Iraq?

Russia’s 2014 aggression against Ukraine was another watershed: Crimea’s annexation was the first unilateral redrawing of borders through use of force in Europe since the second world war. It amounted to throwing crucial multilateral agreements, such as the 1975 Helsinki Final Act and the 1990 Paris Charter, straight in the bin.

China has shown little interest in UN-sponsored laws of the sea, as it seeks to establish its hold on contested maritime territories. North Korea keeps tearing up the 1970 Non-Proliferation Treaty. Add to that the collective failure to deal with the global refugee crisis, and it is clear that multilateralism has been in deep trouble for some time.

Much has been said about the danger hanging over the Paris climate accord. Just as worrying is the fact that institutions created in the aftermath of 20th-century atrocities, in an effort to uphold the promise of “never again”, have increasingly come under assault. Several African states have turned their backs on the international criminal court, a body set up in 2002 as a reaction to the Rwanda genocide and the killing fields of Bosnia.

Play Video 0:32 Drone footage shows Rohingya refugees entering Bangladesh – video

The UN and its council on human rights have been obstructed on crises ranging from Syria to Yemen, not to mention the Rohingya tragedy. European weaknesses were evident when, earlier this year and for the first time ever, an EU statement (on China’s human rights record) was blocked by one of its member states (Greece). It’s not just that authoritarian powers are actively trying to devalue multilateralism; the problem is that there are now fewer and fewer reliable defenders of it.

Are we past the tipping point? Trump may well have his handlers, the so-called “adults in the room”. But much will depend on whether liberal democratic forces in Europe and elsewhere can unite to prevent more institutions from being disembowelled, and crucial agreements from unravelling entirely.

As far as Britain is concerned, the combination of Brexit and of rising leftwing anti-western sentiment does not bode well for the future. Young British Labour voices saying they want to get rid of Nato should be careful what they wish for. Alliances don’t threaten the global liberal order: they are part of what underwrites it.

With America running amok and Britain shrinking into itself, the two countries that have historically set the foundations of the international liberal order may one day find themselves working together to undermine it. Trump is, no doubt, a major problem. But for Britain and the rest of Europe, getting priorities right will matter immensely. The global “arena” theory is not just words. It is fast becoming a reality.

• Natalie Nougayrède is a Guardian columnist