The EU and the US have been squabbling about support for their respective aircraft makers, Boeing and Airbus, for decades. Despite this, the US has never resorted to such heavy-handed tactics with Airbus and the EU as it now has with Canada’s Bombardier, placing thousands of jobs at the firm’s Northern Ireland factory in doubt. And for good reason: the US would have too much to lose from such action. The EU is a big market with a powerful trade authority, and US producers are too dependent on the EU market for the US to risk retaliation. This case gives us a real taste of how the UK will be treated in negotiations over a US-UK trade deal post-Brexit, and how vulnerable the country will be.

Disputes between governments over subsidies to aircraft makers are commonplace. Given the huge barriers to entry into the industry state support is indispensable. Boeing gets its subsidies through US defence spending – which helps to finance the company’s development costs – whereas Airbus has tended to benefit from more direct government assistance. The Canadian government has extended support to Bombardier to develop its new C-series regional jet, leading the US Department of Commerce to claim that the company is selling the jets in the US market at below cost. Both the Canadian and UK governments claim the support they have extended to the firm complies with World Trade Organisation rules. Despite this, the US has taken punitive steps against its two closest allies, imposing tariffs of 219% on the aircraft.

Brexiters assume Britain will face a benign international environment

The UK government, particularly its trade minister Liam Fox, places great faith in a trade agreement with the US, arguing that Britain will get a good deal because of the dense commercial links between the two countries. But trade deals are all about leverage, and leverage is determined by the size of the market. A comparatively small economy such as the UK’s would enjoy little leverage in its negotiation with the US. And if the two countries do not agree a deal, the UK would have to settle disputes with the WTO: cases take years and rulings are often ignored. By contrast, the EU is in a strong position when it comes to disputes with the US; its huge domestic market gives it greater negotiating power. And the US cannot afford to take unilateral action against it of the kind seen in the Bombardier case.

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Moreover, any US-UK trade deal would have to be heavily skewed in favour of the US in order to make it past Congress. For example, in return for a deal, the US would no doubt put the UK under heavy pressure to reform the drug procurement procedures of the NHS – as the largest buyer of pharmaceuticals in Europe, the British health service essentially sets the prices for many other EU markets, and is thus resented by the US pharmaceutical industry, which sees these prices as unfairly low. The US will also put Britain under fierce pressure to fully open its agricultural markets to US food exports. An EU-US trade deal, should it ever come about, would be much more balanced in favour of European interests.

Brexiters assume Britain will face a benign international environment once freed from the EU to take advantage of open markets elsewhere. They take for granted that the UK would be able to rely on the US underwriting the global trading system. This was always naive, but has become delusional with the election of Donald Trump: globalisation can only flourish with wholehearted US support. And that is, at the very least, now in doubt with a more protectionist White House.

With Trump presiding over the Oval Office, engagement with the EU is the best way of defending the UK’s interests and, for that matter, upholding the liberalism many Brexiters claim to support. Indeed, it further heightens the case for Britain remaining in the EU. With globalisation under pressure, the benefits of single market membership are clearer than ever. A US that is less committed to the multilateral trading system also increases the importance of EU membership as a lever to open up markets around the world. In a world where might is right, acting on its own the UK will be a supplicant in any significant trade negotiations.

• Simon Tilford is chief economist of the Centre for European Reform