During the EU referendum campaign Barack Obama warned that Brexit put Britain at risk of relegation as a global trading power. Boris Johnson, then mayor of London, hit back, attributing the US president’s view to “ancestral” dislike of the UK, rooted in “part-Kenyan” heritage. It is not unusual for British politicians to resent being reminded of their country’s junior status in relations with the US (although most manage to express that frustration without nasty racial insinuations). There is no symmetry of clout in the “special relationship”. One side is a superpower, the other is not. Inability to grasp that disparity is a weakness among Eurosceptics.

The belief that Britain would be better off without EU membership is sustained by an inflated sense of the country’s capacity as a solo actor on the global stage. That generates obsession with the idea of trading peer-to-peer with the US, which has led to a misallocation of diplomatic efforts across the Atlantic. Dominic Raab, the foreign secretary, briefly met Donald Trump in Washington this week. Liz Truss, the international trade secretary, was also in the US, promising business audiences that Britain would be “fast-tracking” a trade deal.

Such assiduous attention boosts only the vanity of the ministers involved. It is pitifully naive of Ms Truss to suppose that the tempo of a trade deal can be dictated by Britain. Terms will be set by the superpower at leisure, not the supplicant nation in a hurry. It does not matter that President Trump has said approving things about Mr Johnson, nor even that his secretary of state Mike Pompeo says that the US will be waiting “on the doorstep, pen in hand”. In reality, there will be no favours, just an imposition of brutal realpolitik. It is Congress that can satisfy or frustrate UK preferences, and in that arena the interests of Iowa farmers and US corporations have precedence.

The truth about the balance of power in a UK-US trade negotiation was spelled out this week by former US trade secretary Larry Summers when he said: “Britain has no leverage. Britain is desperate.” That vulnerability will be exacerbated by Brexit. Yet Mr Johnson is putting no effort into relationships with Angela Merkel, Emmanuel Macron or any of the players on the EU council that will settle Britain’s fate in the run-up to the 31 October Brexit deadline.

This is partly an affectation to signal that the negotiating strategy has changed. Continental leaders are meant to observe Mr Johnson’s unflinching march towards a no-deal outcome, and conclude that, unlike Theresa May, he is not bluffing. They are then expected to soften their insistence that the Northern Irish backstop be part of any withdrawal agreement.

Sulking in Brussels will not work any better than sycophancy works in Washington. The EU would prefer an orderly Brexit, but Britain’s negotiating strength decays at an accelerated rate in the messier scenarios. Mr Summers’ equation – leverage decreases as desperation increases – applies to deals with the EU too.

Mr Johnson appears to think that dealings with Brussels are made harder by the formal article 50 Brexit process. The opposite is true. Article 50 is not generous to the leaving member state but it is efficient: a genuine fast track. Ms Truss will experience the slow track once she negotiates with Brussels as a trade minister from a non-EU country.

For decades, British foreign policy was designed on the principle of the bridge between the US and continental Europe. London had a unique mediating function which was valued in Brussels and in Washington, amplifying UK power in both capitals. Brexit knocked down one supporting pillar of that bridge, and yet Mr Johnson appears not to have noticed or not to care as the edifice crumbles and slides into the sea.

It is not too late to adopt a more realistic approach. He might yet engage with EU leaders in a spirit of professionalism and respect. Sadly, those are not qualities often exhibited by Mr Johnson. Diplomacy was once a source of British influence in the world. It should not come as a surprise if the country ends up diminished by its chronically undiplomatic prime minister.

• This article was amended on 8 August 2019 to correctly apply the Guardian’s style guidelines regarding honorifics in editorials.