The Americans know how to make a prime minister feel special. It isn’t hard. Saying “you are special” or words to that effect, usually does the trick. It helps to say it in the White House, within earshot of the British press corps. Westminster hacks and Downing Street aides, most of whom are unhealthily obsessed with US politics, love a Washington summit for the same reason that Harry Potter fans queue to visit the Warner Bros studio in Watford. Standing on the stage where the magic happens is its own reward. That makes Rishi Sunak a cheap date for Joe Biden at this week’s summit. The US president can bestow the normal diplomatic courtesies, while conceding nothing of strategic substance. Downing Street then tells friendly journalists that the two men bonded over baseball, or some other shared cultural enthusiasm, or that their wives did. The prime minister flies home with burnished credentials as the leader of a very important country indeed. The bar for summit success has been set low. It helps that the prime minister isn’t Boris Johnson or Liz Truss, whose bellicose Brexit methods sabotaged transatlantic relations. By negotiating the Windsor framework, easing frictions around Northern Ireland, Sunak atoned for the offence that Biden summarised crudely, but fairly, as “screwing around” with the Good Friday agreement. Sunak’s mission to Washington is also mercifully free of unrealistic speculation about a US-UK free-trade deal. This was an obsession for Brexit enthusiasts. Opening new vistas of transatlantic commerce was meant to outweigh any downside to withdrawal from the European single market. The economics of that proposition never added up, but it was a comfort to Eurosceptics, whose paranoia about London’s submission to Brussels fed a delusion of parity with Washington. Donald Trump nurtured that fantasy. His successor has kiboshed it. Biden’s economic strategy is based around lavish government support for domestic industries, tax breaks for investment and supply chains rerouted to assert US strategic primacy. That buries the model of globalisation that Brexit ideologues had in mind when mapping their buccaneering adventures on the high seas of international trade. Sunak is a disciple of the small-state, anti-intervention school of conservatism. He finds Bidenomics perplexing for that reason alone. But it also highlights the terrible error of quitting the continental bloc in which Britain, by pooling resources with European partners, had a chance of keeping pace with the Americans. If economic competition in the years ahead is going to be an arms race of industrial subsidy, the UK will be outgunned by Brussels and Washington. The counterclaim by keepers of the Brexit faith is that Britain’s isolation is really an advantage, permitting agility and innovation where Europe is staid and sclerotic. A nimbly sovereign nation might lead the way in new sectors. Hence Downing Street has hyped Sunak’s interest in AI ahead of the Washington trip. The prime minister has been consulting tech bosses about awesome new computing powers coming on stream. He has been pondering how best to manage the development of machines that might, within years, rival nuclear weapons in their capacity to cause harm in the wrong hands. He has concluded that Britain can lead the world in this field, and that London should be the capital of global AI governance. He will raise all of this with President Biden, we are told. The idea of an international AI regulator – equivalent to the International Atomic Energy Agency in Vienna – is perfectly sensible. London could make a respectable bid to host it. But so could other cities. Either way, it won’t be decided over coffee on Wednesday night. Visiting leaders “raise” all sorts of things with their hosts. It is a diplomatic euphemism for questions brought to the table with no expectation of answers. Things are “raised” for the benefit of an audience back home, so the leader who doesn’t really set the agenda can claim to have put some item on it. Under a friendly (or credulous) media lens, the prime minister is thus projected from the margins of international influence into the centre. Something similar happened last week, when Sunak attended a summit of the European Political Community (EPC) in Moldova. The EPC was first convened last year by the French president, Emmanuel Macron, in response to Russia’s invasion of Ukraine. It is envisaged as a forum where EU and non-EU heads of government can discuss pan-continental issues. That is no substitute for the seat (and the veto) that Britain used to have at European Council summits, but it is better than nothing. Ukraine was the focus of discussions in Moldova. Except, that is, when Sunak raised the topic of illegal migration. His unilateral digression was then spun by Downing Street as Britain “taking the lead” on a vital issue; putting it “at the top of the international agenda”. This fiction was transmitted by various UK media outlets, as if all of Europe’s leaders huddled round their British counterpart while he laid down the law on small boats crossing the Channel. Preposterously, GB News even reported it as a “migration meeting”. At least Sunak was invited to Moldova. There had been no British representation the previous week at a meeting in Sweden of the EU-US Trade and Technology Council. This, too, is a relatively new institution. It was launched in June 2021 by Biden and Ursula von der Leyen, European Commission president, to coordinate policy on “global trade and technology” between Washington and Brussels. The most recent gathering discussed a code of conduct for AI development. That is exactly the conversation Sunak thinks should be happening in London. But if Americans and Europeans are already having it somewhere else, why should they move it? What does Britain offer for just a seat in the room? To raise the question is not to deny that a UK prime minister has clout. There is heft in the office of the leader of a G7 economy, with a nuclear arsenal and a permanent seat on the UN security council. Biden makes time for Sunak because the relationship between the two countries is important. When it comes to defence and security cooperation, it is one of the sturdiest alliances in the world. But friendship is not the same as influence. It is a bald strategic fact that Brexit makes a British prime minister less useful to Washington. Without leverage in Brussels, Sunak is not in a position to broker deals with Biden. Instead, he pays tribute. That can be spun into something special for the parochial Westminster audience that doesn’t want to admit that Britain is smaller outside the EU. The message will get through eventually. There are only so many angles for making the margins look like the centre. There is only so long Britain can fake being a global power if it isn’t a player in Europe. Rafael Behr is a Guardian columnist