As well as enough money to build a new hospital every week post-Brexit, the Leave campaign promised to relieve the NHS of the pressure it is put under by 'health tourism' and the arrival in Britain of hundreds of thousands of public-service-hungry migrants each year. It now seems the NHS is as unlikely to benefit from restrictions on EU immigration to Britain as it is to receive an extra £350 million a week. The amount that would be saved by not treating EU migrants would make no dent in the NHS’s financial problems, while a lack of EU workers would mean fewer staff on overworked NHS wards.

The Nuffield Trust estimates that migration from the EU accounted for £160 million of the rise in NHS costs between 2014-15 and 2015-16 – a negligible amount compared to the £1.6 billion extra spent on new technologies and improvements in standards of care, and the £2.8 billion increase from inflation and rising wages.

Meanwhile, the most recent figures from the National Audit Office show a shortfall of 5.9 per cent between the number of NHS staff required and the number available to work – equivalent to 50,000 full time members of staff. For nurses, midwives and health visitors, the shortfall is as high as 7.2 per cent. The staffing crisis is likely to get worse, as one in three nurses are set to retire within the next 10 years, according to a report by the Institute for Employment Studies. The shortfall is the predictable result of chronically underfunded nurse training and increased demand for nursing services.

EU nationals make up 55,000 of the 1.3 million people who work for the NHS, including 10 per cent of doctors and 4 per cent of nurses. ‘The NHS cannot survive without the tens of thousands of dedicated health staff from across the EU currently working here,’ Unison’s head of health, Christina McAnea, said. ‘Following the referendum, workers from Europe – and elsewhere – need to know they are valued hugely, both by the NHS and the people they care for.’

Terence Stephenson, the chair of the General Medical Council, said that Brexit will not affect the status of EU doctors currently registered to work in the UK. Jeremy Hunt, the health secretary (still), and senior figures in the NHS have made public statements of support for NHS staff from the EU.

But incidents of racism directed at NHS employees by patients have risen since the referendum, with the Nursing Timesreporting that European midwives have been abused or told to ‘go home’, and that other EU nurses are planning to leave the UK within the next few years because of the fear of racist abuse.

Even if existing NHS staff from the EU are persuaded to stay, Brexit threatens to cut off the supply of new European recruits. More than 60 per cent of healthcare trusts reported actively recruiting nurses from outside the UK in the past year, and before the referendum, further recruitment from the EU was planned for both doctors and nurses.

‘With the uncertainty around the status of EEA workers in the UK, the recruitment pipeline from Europe is likely to be hit hard,’ according to Rachel Marangozov, the lead author of the IES report. ‘Many nurses already in the UK, as well as potential recruits in countries like Spain and Italy, will be concerned about their future prospects if their status in the UK remains uncertain.’