President Donald Trump tweeted on Tuesday that he was working on a potentially “very big & exciting” trade deal with Britain that would shame the “very protectionist” European Union. He is right that such a deal could be politically advantageous for both governments. For British consumers, though, it may deliver little more than chlorinated chicken.

UK International Trade Secretary Liam Fox, whose talks with US trade officials prompted Trump’s tweet, estimates that a deal could boost trade between the countries by $52.2 billion (about £40 billion) a year by 2030. That is ambitious but not outlandish: back in 2013, when the United States was negotiating the ill-starred Transatlantic Trade and Investment Partnership with the European Union, a British-commissioned study found that it would increase trade between the countries by some £38 billion a year by 2027.

The TTIP is a logical template for any new deal. Britain has not negotiated a trade agreement since it joined the EU, so piggybacking on the experience of the bloc’s master negotiators makes sense. That said, achieving Fox’s trade-volume goal will require going to the limit of what the TTIP contemplated. That means removing all tariffs and 50 per cent of all “actionable non-tariff barriers”, including 75 per cent of restrictions on chemicals, vehicles, and business and technology services. Among the highest non-tariff barriers are those for food: they increase US importers’ cost of accessing the British market by an estimated 46 per cent.

The food issue is likely to be the most controversial. The TTIP died in part because Europeans — Germans, in particular — feared a drop in quality standards and the growing power of US multinationals. In Britain, EU membership has raised the quality of local produce and, at least in London, improved the availability of good food from Italy, France and Spain. Anyone who has had a chance to compare the food in the average European store, including a Tesco in Britain, with its American counterpart knows how obvious the quality and taste gap is.

Understandably, the public discussion of a potential deal with the US has focused on food, and specifically on the American practice of washing chicken carcasses in a chlorine solution — banned in the EU since 1997. Pressed by pro-EU campaigners to eat chlorinated chicken on his US trip, an irate Fox remarked that the media were “obsessed” with an issue that would not come up until a late stage in the talks.

But the British can be forgiven for worrying about American chicken flooding their supermarket shelves: even if it is safe and 20 per cent cheaper than poultry produced in Britain to EU standards, many Britons would rather stick with the kind of food to which they have become accustomed. And no matter how many scientists defend genetic modification and the various additives that are permissible in the US, freeing up the markets for these imports will not be popular.

Meanwhile, the balance of power in the negotiations does not bode well for the British side. It’s the smaller market, accounting for less than 3 per cent of US trade, and the government of Prime Minister Theresa May needs a quick success with a significant trading partner. Fox has already been building up expectations: in a recent article in The Sunday Times, he promised that the US deal would be “just the beginning” of opening post-Brexit Britain to global trade.

Trump, by contrast, is in no hurry. A deal makes sense for him only if he wins in zero-sum terms. US negotiators may not take Trump’s urge to stick it to the EU too seriously, given that annoying the world’s largest economic bloc is not in the country’s strategic interests. But they will not be able to ignore Trump’s desire to do only deals that improve the US trade balance. Trump likes imagining trade in terms of tangible objects, such as cars or, yes, chickens. So, perhaps for a better deal on services, Britain will need to give on things such as cars and food — and the British Government will not rule out changing some quality regulations to do a deal.

Weak as Britain may be in the Brexit talks, it has a stronger hand than with the US. It is a bigger trading partner, absorbing between 8 per cent and 17 per cent of the exports of the remaining 27 EU nations — depending on the measurement method. And EU negotiators have not attended the Trump school of economics: they are not aiming to increase their trade balance with Britain at any cost.

Britain ought to concentrate on the more important trade relationship with the EU. With the right concessions, it can still get a good deal. Hoping for a victory with the outwardly friendly Trump Administration is delusional.

• Leonid Bershidsky is a Bloomberg View columnist. He was the founding editor of the Russian business daily Vedomosti and founded the opinion website Slon.ru