For close observers of the Brexit process, the only thing that was surprising about the EU’s rejection of the so-called Chequers deal at the European Council meeting at Salzburg was that so many people, including the Prime Minister, were surprised. It had been clear from the beginning that it was going to be unacceptable and, even if the EU had accepted it, there was no realistic prospect of it being agreed within the Conservative party, let alone the UK Parliament. Indeed, within days of agreeing it in Cabinet, several ministers resigned.

At her press conference in Salzburg Theresa May was visibly upset and, back in Downing Street, her anger was palpable as she rejected the few feasible options. She had expected to get, if not a ringing endorsement from the EU27, at least some warm words. After all, she had heard several already welcome it. Realising her domestic vulnerability, her EU counterparts have been trying to be as supportive as possible, at least to help her get past the forthcoming Conservative party conference. A leadership challenge would set the process back by months, taking up time that no is longer available. So what went wrong?

First, the UK (or at least most of its politicians and journalists) seem to have misunderstood that the welcome for Chequers arose from the sense of relief that, after more than two years, the UK had finally written down what it wanted. It was not an expression of enthusiasm. Until then all they had to go on were speeches written for domestic consumption that displayed a profound ignorance of how the EU works and were widely derided as being as realistic as a demand for unicorns.

The initial Brexit white paper was thin on detail, to the extent of having numerous blank pages, and at least initially, containing several errors. Its second one was little better, being described as containing “muddled thinking, desperation, and fantasy.” Most recently, its so-called “No deal” papers were nothing of the sort as they assumed that, even if no overall deal could be reached, individual EU member states would be willing to sign up to a multiplicity of smaller agreements. This was cherry picking on an industrial scale. And once again, there was little detail, in marked contrast to the EU’s extremely detailed notices to operators, which the UK government seemed not to have read, to say nothing about some fundamental errors, such as not knowing which countries are in the Schengen Agreement. In fairness, this is understandable. A recent Institute for Government report describes the lack of preparedness in the Department for Exiting the EU. Other accounts describe morale at rock bottom, exceptionally high staff turnover, and staff waiting months to get security clearance to read documents that have been classified as secret, such as the earlier reports that were too sensitive to release because they revealed facts such as how fishing was concentrated in coastal communities.

Second, the Chequers agreement could only ever have been a starting point as it was clear that many of its provisions were contrary to the European treaties. These treaties could be amended, but the process would take years and several countries would have to hold their own referendums.

Third, the UK had agreed at the outset of the negotiations that they would be sequenced, with discussions on a future trade deal following a withdrawal agreement. Although some aspects of this withdrawal agreement have been agreed, there has been no progress on some others. One of these, Ireland, seems to have been the trigger for the EU response at Salzburg.

The UK had signed up to a backstop position, in which Northern Ireland would remain in the single market and customs union if no other agreement was reached and had spent the intervening months trying to disown its commitment. The EU had been asking the UK repeatedly for key information on trade flows between Great Britain and Northern Ireland but nothing was forthcoming and, when Theresa May revealed to the Irish Taoiseach at Salzburg that she may not be able to propose a solution before November 2018, other European leaders were filled with a sense of despair. The patience of EU27 leaders had already been tested by UK ministers touring television studios arguing that a future government could change anything that was agreed anyway and by the UK’s failed attempts to go behind the back of Michel Barnier thinking it could divide and rule. Theresa May simply was not getting the message and warm words would only prolong the agony.

So where now? The Prime Minister’s statement on her return offers little to assist us. Despite the almost universal rejection of the Chequers agreement, she intends to stick with it. Perplexingly, she claimed that the EU had made no concrete proposals, even though it had made the options clear months previously in a pictorial form and has never deviated from this, precisely because it cannot without a Treaty revision. She also reiterated her argument that the UK was preparing for a “no deal” situation, even though it was clear to almost everyone that this could only last for a few weeks because of the massive disruption this would bring. The UK’s “no deal” papers, as noted above, simply confirmed the scale of the crisis that would arise, despite the attempts of the authors to hope for the best, mainly by assuming that somehow hundreds of separate agreements could be reached in a few months even if an overarching one remained elusive. This is completely uncharted territory.

At a time like this, it is essential that those responsible for safeguarding the health of the British people are heard. As they examine the risks involved, the picture only becomes bleaker.

It was always clear that there was a threat to medicines supplies but the realisation that almost all insulin is imported from other parts of the EU has concentrated the minds of those with diabetes. Others have highlighted the threat to supplies of flu vaccine, trucked in from Normandy. The threat to medical isotopes was also known but a new and detailed examination has shown the problems to be even worse than anticipated. Supplies of medical equipment will be severely disrupted and those responsible for complex equipment in hospitals have realised that the engineer who flies in from Germany when they go wrong will be providing a cross-border service, with no legal basis for doing so, so they simply won’t be able to come.

NHS organisations are struggling to prepare but few have made any progress and they lack even the most basic guidance from the Department of Health and Social Care, presumably because it knows little more than anyone else. Then there is the threat to food supplies. Reassurance that something will work out seems unconvincing to those who have experienced the disruption that accompanies British winters or truck drivers’ strikes. The UK’s “just in time” operation does not adapt well to disruption.

Given the failure of the politicians to find a solution, the case for a further referendum becomes compelling. This has now been backed by the BMJ, the BMA, the Royal College of Nursing, and many others. If someone has a better solution, then they should be listened to with respect. But time is running out.

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

Competing interests: None declared.