A UK-US trade agreement was always going to be a tough sell. American Ambassador Woody Johnson’s comment to Andrew Marr on Sunday that healthcare would need to be on the table in any future trade talks only served to make agreeing a fully-fledged deal all the more difficult.

That the US will drive a hard bargain in any future negotiation with the UK should come as no surprise. Only the EU, and perhaps China, have the economic heft to negotiate on near-level terms with the Americans, and even they struggle. The US’s objectives for its negotiation with the UK were published in February and — with the caveat that they were largely produced for a domestic American audience, shorn of all notion of compromise — are strikingly ambitious in their demands.

For example: alongside normal talk of tariff and quota removal, the UK must jettison food hygiene rules that currently restrict US exports of beef, pork, chicken and dairy; rules stipulating which products qualify for tariff-free treatment under the agreements must specifically incentivise production on US territory; and the agreement should include a mechanism allowing for the US to take appropriate action if the UK negotiates an agreement with a “non-market economy” (see: China).

It should be noted, however, that healthcare is not explicitly mentioned. Despite long-running fears of a US trade deal-inspired privatisation of the National Health Service, public services are largely carved out of free trade agreements, and that is unlikely to change. Absent a free trade agreement, American healthcare providers already compete to deliver services in the UK where the NHS puts out contracts to competitive tender. This is not without its own controversy, but was a unilateral decision made by a British government seeking value for money.

However, US demands regarding reimbursement regimes for pharmaceuticals and medical devices give greater cause for thought. The US has long taken issue with the fact that the NHS’s approach to drug procurement — where it makes its own assessment as to the fair value of the drugs it buys — pulls down prices worldwide. Previously, in negotiations with Australia and New Zealand, the US backed away from trade asks on drug pricing in order to get agreements over the line, but due to the NHS’s global significance and market power, the incentives for the US to push the UK harder are more pronounced.

Regardless, perception is more important than reality when it comes to selling an agreement, and so long as the British public believe the NHS to be on the table any deal will struggle for legitimacy.

In practice, we will not know whether the UK will be in a position to even begin negotiations with the US until at least the end of October. Without greater clarity on the nature of the UK’s future relationship with the EU, it is impossible to enter into substantive discussions with the US. This is because any relationship with the EU comprehensive enough to ensure an all-UK solution for Northern Ireland, for example, would greatly restrict the UK’s ability to concede to the US’s demands and get an agreement over the line.

Yet even if the UK is to enter into a looser economic relationship with the EU following an ordered withdrawal, we should not assume that a deal with the US will be easy to come by. Agriculture remains a contentious sticking point and Conservative fears of upsetting their rural base will be difficult to overcome. Equally, stories of US chlorinated chicken and hormone beef have already permeated the public consciousness.

While Trump could agree to a bare-boned agreement that excludes agriculture and controversial topics such as food safety and drug pricing, just to say he had successfully negotiated something, it seems unlikely. The UK is not the end-game for the US. Its ultimate ambition is to open up the bigger EU market. For the UK to move to a more American approach would set a regional precedent, grant the US a regulatory foothold in the EU’s backyard, and push back against the EU’s increasingly global regulatory hegemony.

Perhaps the only event that could cajole MPs and the British public into holding their noses and signing on Trump’s dotted line is a no-deal Brexit. The subsequent upheaval and economic uncertainty of no-deal would likely see the UK grasping for anything that looks like an economic lifeline. (Although there is no reason to think that a trade deal with the US would come close to offsetting the negative economic shock of any kind of Brexit.) This might also part-explain Trump’s propensity to talk up no-deal.

Yet British MPs pining for such an outcome should think twice. Trump is not to be trusted. Just see what happened with Mexico: even though it recently agreed to a revamp of its existing trade agreement with the US and Canada, Trump has now threatened to levy a 5 per cent tariff on all Mexican exports to the US unless illegal immigration comes to a halt. Even if a no-deal Brexit does happen, and a lopsided US-UK free trade agreement is concluded, Trump may immediately come back asking for more.

Sam Lowe is a senior research fellow at the Centre for European Reform. He tweets @SamuelMarcLowe