The European Health Insurance Card symbolises the many benefits that the European Union brings to its citizens. It allows tourists to obtain healthcare when they are visiting another member state just as if they lived there permanently. And it is only one, albeit the most visible, element of a comprehensive legal framework covering healthcare among those moving within Europe. Other elements include provision for the hundreds of thousands of British pensioners who have retired to sunnier climates and those who depend on dialysis, for whom a trip abroad would otherwise be completely unaffordable.

Unsurprisingly, it is one of the benefits of European Union membership that the British government hopes to retain. On many occasions, British ministers have expressed the intention to find some way of keeping the system going. But can they? I was recently asked this question when giving evidence to a House of Lords committee. This is an occasion where it pays to do your homework, as the members of that committee, including a former chief executive of the NHS and a head of the diplomatic service, can be expected to ask extremely penetrating questions. As a result, I have spent several long evenings reading through numerous arcane treaties and dense legal reports. And the conclusion I’ve reached is that, even if it is not totally impossible, the British aspiration is, to say the least, extremely complex and certainly unlikely to be achieved any time soon.

The reason is quite straightforward, once you think about it. European governments did not adopt mechanisms to allow their citizens to access healthcare elsewhere for reasons of altruism. The welfare of a drunken participant in a stag party in Prague or Krakow never entered their thinking. Instead, their goal was to support one of the European Union’s four fundamental freedoms, the freedom of movement of people. Quite simply, a single European labour market would be impossible if those moving for employment, either permanently, or as was initially the case with those working in the coal and steel industry in the French-German border, on a daily basis, could not be assured that they would be looked after if they became ill. Moreover, arrangements to provide health cover were only part of a much larger package, covering areas such as pension entitlements, occupational and industrial injury benefits, and maternity benefits. Consequently, arrangements to enable people to obtain healthcare fall squarely within the European Union’s social security remit.

Obviously, if the arrangements to provide health cover are there to facilitate the free movement of people, then it is difficult to see a rationale for maintaining them in respect of a country that has decided to restrict free movement. In other words, by taking back control of its borders, the United Kingdom has said very clearly that it wants to opt out of all the arrangements that go with that. Although, of course it hasn’t. It wants to keep the health coverage, yet another example, among many, of wanting to have one’s cake and eat it.

But surely, the supporters of Brexit will argue, if the European Union refuses to continue these arrangements, it will be doing so to punish the British. This has now become the standard refrain when they are told that something will no longer be possible. The reality is, that as healthcare is a national competence, the European Union has no powers to make an agreement with a third country, as the UK will become. The only such agreements that are in existence are the EU-EFTA Treaty, with Iceland, Norway, and Liechtenstein, and the EU-Switzerland Treaties. In both cases, the other countries are required to adopt European Union law, without having any say in its development. They are also required to accept free movement of people. True, both of these arrangements lie outside the scope of the European Court of Justice (ECJ), hated by the supporters of Brexit, but the former is overseen by the EFTA Court, which almost always follows the jurisprudence of the ECJ. The absence of a clear dispute resolution system in the latter, coupled with widespread concerns about the nature of the agreement between the EU and Switzerland, mean that a similar arrangement with the UK is virtually impossible.

Given that healthcare is a national competence, European Union member states are allowed to make bilateral agreements with any country they choose. The United Kingdom already has a number of these, mainly with its dependent territories and with Australia and New Zealand. Until 2016 it had similar arrangements with the states that emerged from the USSR and still has them with the countries that were part of Yugoslavia. However, the persistence of these arrangements seems almost certainly because the work of terminating them has never reached the top of the agenda of the relevant department within the UK government, even if it was clear who that was. Other member states have dozens of such arrangements, entered into for a variety of reasons. In some cases, they reflect links going back to the colonial period. Others, involving countries aspiring to EU membership, act as a symbol of this aspiration. A few more have been adopted under pressure from large corporations, seeking to ensure provision for their workers in countries such as India. However, what is striking is that the UK has not entered into any such agreements for many decades.

The clear implication is that, if the UK wants to maintain some sort of healthcare coverage for its residents in the rest of the EU, including those nationals of other EU member states legally resident and working in the UK when they return home, then it will have to negotiate bilateral agreements with each of the other 27 governments. It is not obvious that all of them will see this as a priority. An alternative would be to wait until all of them had agreed among themselves about a mechanism to cooperate with external countries, but this could take a very long time. It is something that has been discussed for many years, particularly with respect to the countries of North Africa, many of whose citizens work within the EU. However, it has never been possible to reach agreement even on limited provisions covering issues such as pensions. It may also be possible to find a way of agreeing something with groups of member states, such as the Ibero-American agreement, involving Spain, Portugal, and a number of countries in Latin America. However, even this is extremely limited in scope compared to what exists at present.

There are a number of other important obstacles. First, the existing system is not stand-alone, but instead builds on a considerable body of other European law, in areas such as data protection and liability when things go wrong. All of these would have to be agreed between the UK and the EU, but many of them relate to the operation of the single market, which the UK government has rejected. Their application within EU member states has to be compatible with EU law, overseen by the ECJ, which would give the court at least an indirect say in their use, something again rejected by the UK government.

The problems related to the EHIC help explain why the supporters of Brexit are most comfortable at the level of generalities. Any attempt to get into the details of what they want rapidly hits the wall of reality. Moreover, given the inability of the British team to come up with any feasible answers to the big questions months after Article 50 was triggered suggest that, if they ever do get into the detail, they are likely to be occupied for decades. Indeed, in comparison, Charles Dickens’ legendary case of Jarndyce v Jarndyce, which continued through the courts so long that “that no man alive knows what it means” may come to be seen as a sprint!

Martin McKee is professor of European public health at the London School of Hygiene and Tropical Medicine.

Competing interests: None declared.