President Trump has reached out a tiny hand and continued his promise to support Brexit Plus Plus Plus with a UK-US trade deal. But as the Prime Minister heads over to the White House as the first foreign leader to meet with the new administration, it is doubtful such a deal, negotiated quickly, will have that much of an impact on UK exports.

As we start the march towards Brexit, the rhetoric has increasingly revolved around Britain taking its place once more as a great global trading nation, fearlessly finding new markets to do business with. The reality, however, looks somewhat different. Liam Fox, Britain’s International Trade Secretary, came to a similar conclusion last Autumn when he lamented that some UK businesses seemed to prefer playing golf to expanding into new markets.

The more pertinent issue is whether this new US trade deal (or, in fact, any trade deal Dr Fox manages to make from his list of 12 “fast-track” countries) will be the silver bullet we need for a Brexit triumph. Because what if it is not the tariffs or rules that dampen down UK businesses’ appetite to reach new markets, but the simple fact that they don’t want to export much in the first place?

That brings us to the potential UK-US deal. We have heard much of how it can be done quickly, how it will involve the reduction or dismantling of tariffs, and how we should aim for relaxed working restrictions for UK and US citizens. But how much of an impact would this actually make on UK businesses? It is true that the US is a huge trading partner of the UK – our biggest individual country market – and yet the next four countries on the list are all in the EU and, combined, are almost double in share of the total UK export market. Trade really is often done with those closest to you.

Even if we are not held at a disadvantage in the certainty we need a new deal fast, and even if Trump’s constant messaging of American jobs first is more nuanced in reality than in rhetoric, will British businesses actually benefit hugely from a trade deal with the US?

Research published this week by the Federation of Small Businesses suggests not, highlighting that 54% of small businesses would not even consider exporting. 99% of UK business is made up of small businesses. If over half do not want to or will not even consider exporting, that is a big barrier to our trading success. It is not a free trade agreement that is needed, but a sea-change in business attitude and government support.

In this same survey, only 9% of small businesses whigh had never exported but whigh would consider it thought tariffs or tariff issues were a potential challenge. Bigger deterrents included: finding the customers, marketing, market knowledge, and knowing where to go for support.

93% of small business exporters export to the EEA, compared to 61% to North America. When access to many of the markets in the EEA becomes trickier, there is no guarantee that exporters will simply switch their attention to the market across the pond. Given the notable reluctance of smaller businesses to export anyway, to anywhere, it seems unlikely that they will suddenly all rush stateside.

The lack of exporting appetite has been an issue grappled with by UK trade ministers for years. A new trade deal could help with the rhetoric of Britain finding a new role in global trade, but its real impact on UK exports remains in serious doubt. The fundamental obstacles making UK companies reluctant to export are not going to be improved by whatever promises May can extract from Trump in the Oval Office. Instead, more hard work is needed to support companies, provide the export finance, and reduce the more pervasive barriers often found in regulation and hidden behind tariffs.

Without that, a UK-US trade deal will be no more than a shiny bit of showmanship. Much like Trump himself.