It was not off the cuff. It was clearly meant. But was Donald Trump right to claim Theresa May’s Brexit deal meant the UK after 29 March 2019 “may not be able to trade with us”?

The UK is the fifth largest export market for American goods. British exports to the US are worth about £100bn a year to the UK economy, according to the Office for National Statistics, more than twice that of any other country.

There is nothing in the withdrawal agreement or the political declaration that is likely to heavily impact on that baseline of trade, although US direct investment into the City of London will decline as the EU “passports” allowing UK-based bankers and traders to offer services across member states are taken away.

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The US president, who during his campaign for the White House feted Nigel Farage, was more likely suggesting that the Brexiters’ great prize of a US-UK comprehensive trade deal would be precluded by the deal struck by May in Brussels.

The international trade secretary, Liam Fox, claimed last summer that bilateral US-UK trade could rise by £40bn a year by 2030 “if we’re able to remove the barriers to trade that we have”.

Those barriers to transatlantic trade are tariffs and standards.

Trump has complained that EU tariffs on imported American cars, for example, are punitively high. In the idealised US-UK trade deal, an unfettered Britain could seek to undercut those while negotiating better terms for its exports to the US.

In terms of standards, Fox has suggested he would be open to allowing US chicken that has been cleaned using chlorine – a practice banned by the EU – to be sold to British consumers, as part of a general relaxation of such non-tariff barriers to transatlantic business.

The Brexit deal endorsed by the EU’s heads of state and government at the special summit on Sunday, which will be voted on in the House of Commons on 12 December, does indeed set up significant obstacles to such trade liberalisation.

The withdrawal agreement foresees a 21-month transition period during which the UK will stay in the single market and customs union, without any representation in the EU’s decision-making institutions.

In the highly likely scenario that a EU-UK trade deal is not close to ratification by July 2020, the EU and UK would jointly decide at this “rendezvous” point whether to extend the transition period for up to two years.

Play Video 0:40 Trump says UK ‘may not be able to trade with US’ under May’s Brexit deal – video

During this transition, short or long, the UK would continue to be bound to the EU’s commercial policy, common external tariffs, and standards.

It would theoretically be possible for Fox to start negotiations with Washington about a future trade deal, but the UK’s customs relationship with Brussels will not be clear until very late in the transition period, making it almost impossible for any serious groundwork to be done.

Brussels and Downing Street could alternatively, at the rendezvous point or after the extended transition period ended in 2022, allow the backstop solution for avoiding a hard border on the island of Ireland to come into force, if a final trade relationship with the EU was still not settled.

The backstop is an all-UK customs union with the EU, with commitments for a level playing field to ensure Britain does not lower its environmental, social and labour standards.

Such a customs union would again bind the UK into the EU’s common external tariffs on goods, precluding the sort of deal envisaged by Brexiters. Fox could only busy himself with trade deals on services, in an attempt to lower barriers of trade for the City of London-based firms selling themselves in the US.

When the British prime minister insisted on Tuesday that the UK would be able to strike trade deals in the future, she was assuming that a comprehensive EU trade deal would be settled at some point to relegate the transition and backstop to history.

But the political declaration suggests the backstop envisioned in the withdrawal agreement will be built on during the trade negotiations to come. It is said to be the baseline for the future trade relationship, as it is only by replicating and enhancing such a customs union that the problem of the Irish border can be resolved, and crucial cross-Channel supply chains protected.

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Confusingly, the political declaration further states that the UK will have an independent trade policy in the future. It is extremely difficult to see how both of those statements can be right. The last two years of negotiations have shown how difficult it is to square the circle.

Despite all this, transatlantic trade liberalisation could still be on the cards. Trump has been seeking a trade deal with the EU, and has been threatening tariffs on the European car industry in order to attain such a prize. The UK would likely be covered by such an EU-US deal should it maintain a single customs territory with the bloc. Brussels has a policy of pushing its new trade deal partners to allow countries such as Turkey, with whom the bloc is in a customs union, to enjoy similar beneficial terms as its member states.

The only problem: no one predicts that trade talks with Trump, for those inside or out of the EU, will be easy. It is an analysis only confirmed by the US president’s latest damaging intervention in the Brexit debate.