Nursing vacancies are one of the "biggest threats" facing the health service, a leading think tank has warned.
One in 10 nursing posts are unfilled, the Health Foundation said.
The remarks come as the nursing and midwifery regulator announced that it would be making it easier for foreign nurses to come to work in Britain.
The Nursing and Midwifery Council (NMC) said that it was planning to relax rules on when nurses from outside the EU can register to work in Britain after qualifying.
It comes as new analysis by the Health Foundation showed plummeting numbers of EU nurses coming to work in the UK.
Health Foundation analysis of NMC figures found the number of new nurses coming from the EU to work in the UK has dropped by 87% from 6,382 in 2016/17 to 805 in 2017/18.
But new data from the NMC suggests there has been an increase in foreign nurses and midwives coming to work in Britain from outside of the EU.
At the end of June 2018 there were 69,425 nurses and midwives on the register from outside the EU compared with 67,534 in July 2017.
Meanwhile, the NMC announced that it was reviewing its registration processes for people trained outside the UK.
Plans include allowing nurses and midwives from outside the EU to apply to join the register immediately after qualifying - rather than having to wait for at least a year, as is currently the case.
Emma Broadbent, director of registration and revalidation at the NMC, said: "The fact remains that the UK workforce is under significant pressure and it's vital that we continue to enable the right people with the right skills and knowledge to join our register in the quickest and safest way possible.
"That's why the time is right to look at the application processes for overseas nurses and midwives as whole, to ensure that it's truly fit for the future.
"Our proposals will make the application process simpler and fairer while continuing to maintain the high standards required to join our register."
Meanwhile, a poll of more than 2,000 British adults, conducted on behalf of the Health Foundation, found 79% do not believe the NHS has enough staff to provide current services.
"The huge drop in the number of EU nurses coming to work in the NHS following the referendum is a stark reminder that we must never take overseas staff for granted," said Anita Charlesworth, director of research and economics at the Health Foundation.
"We must make sure that the health service is an attractive and welcoming place to work for both international and home trained staff.
"With one in 10 nursing posts vacant, this is one of the biggest risks facing the NHS.
"Uncertainty about the position of EU staff after Brexit adds to the challenge of securing enough nurses to sustain high quality care."
Figures for the final quarter of 2017/18 from NHS Improvement show the high levels of vacancies across the NHS in England.
There were 35,794 nursing vacancies, which equates to 10.2% of posts in the field.
Janet Davies, chief executive and general secretary of the Royal College of Nursing, said: "Regardless of how people voted in the Brexit referendum, this shows they see the value of nurses from around Europe and know we desperately need to keep them.
"Uncertainties and nervousness around Brexit have seen EU nurses leaving in droves. When there are 40,000 vacant nurse jobs in England alone and falling interest in studying nursing, the public are right to worry about the dangerous consequences of this understaffing.
"Voters and taxpayers are sending a clear message to the Government - a nurse who trained in Barcelona is as welcome as a nurse who trained in Bradford, not least when the shortage is so great.
"Ministers must give greater clarity on the immigration restrictions professionals will be subject to if they wish to work in the UK post-Brexit.
"The very latest figures on nurses from the wider world reveal a small but encouraging increase that we will continue to monitor.
"While the NHS has always relied on the contribution of its international workforce, there is no alternative to a proper domestic plan and that is still seriously lacking."
A Department of Health and Social Care spokeswoman said: "The NHS is nothing without its brilliant workforce and staff from overseas will continue to have a vital role in the NHS long after we leave the EU.
"We are also increasing the number of home-grown staff with a historic 25% increase in training places for doctors and nurses - meaning the NHS will have the staff it needs to continue providing world-class care in the future."
Copyright (c) Press Association Ltd. 2018, All Rights Reserved. Picture (c) David Jones / PA Wire.