The head of NHS England has urged the government to reconsider immigration rules that will see lower-earning nurses, rather than ballet dancers, from outside the EU deported at a time when the profession faces a shortage.

The policy has already been criticised by employers’ groups and the nurses’ union, which have said it is a recipe for chaos that could cost millions in recruitment.

They have called on the Home Office to add nurses to the list of shortage occupations, which are exempt from the new rules, and reconsider the £35,000 salary threshold. Under the rules, workers from outside the European Economic Area who are earning less than £35,000 after six years in the UK will be deported.

On Tuesday, NHS England’s chief executive, Simon Stevens, became the most senior figure within the health service to enter the fray.

He told the Institute of Directors (IoD) annual convention in London: “Understandably we’re having a national discussion about how to get immigration right. My responsibility is to point out that, at time when the need for nurses is growing, when publicly funded UK nurse training places will take several years to expand, and when agency staff costs are driving hospital overspends right now, we need to better join up the dots on immigration policy and the NHS.

Simon Stevens: ‘Most nurses I speak to struggle to understand why our immigration rules define ballet dancers as a shortage occupation but not nursing.’ Photograph: Alamy

“However, most nurses I speak to struggle to understand why our immigration rules define ballet dancers as a shortage occupation but not nursing. And most hospitals tell me the idea that we would seriously consider deporting some of our most experienced and committed nurses solely because they’re not earning £35,000 clearly needs a rethink.”

The Royal College of Nursing has claimed that, as things stand, up to 3,365 nurses, who cost £20.19m to recruit, could be affected.

But the union says that figure could rise to 29,755 nurses, costing more than £178.5m to recruit, by 2020, if workforce pressures lead to increased international recruitment.

It says there is a lack of home-grown people trained to do the job and that new rules capping the amount spent on agency workers make overseas recruitment a vital outlet.

Stevens’s intervention came as the home secretary, Theresa May, told the Conservative party conference in Manchester that Britain must work harder to control immigration, in a speech criticised by the IoD as pandering to anti-immigration sentiment. The health ecretary, Jeremy Hunt, also claimed the Tories were the “true party of the NHS” and told its employees: “We are proud of every single one of you.”

Stevens’s comments won him plaudits from the lobby group NHS Employers, which has been at pains to point out the difficulty the new rules will cause its members.

Its chief executive, Danny Mortimer, said: “We warmly welcome the important intervention made by Simon Stevens in highlighting the value of migrant nurses and doctors in the NHS who have contributed a significant amount to the way we deliver care to our patients. NHS Employers has written to the home secretary, Theresa May, to highlight that many NHS Trusts are facing a shortage of nurses going into winter as the Home Office refuses to grant visas to nurses from outside the EU.”

He said plans to train more nurses domestically would not deliver qualified professionals until 2017.

Janet Davies, chief executive and general secretary of the RCN said: “There is now a consensus across the health service that the Home Office must make a change.

“It is an irrefutable fact that rising demand for health care, a shortage of home grown nurses, and new rules limiting the use of agency staff mean the NHS is reliant on overseas recruitment to provide safe patient care.

“Ignoring this issue any longer would be irresponsible, illogical and bad for patients.”

A Home Office spokeswoman said it made sense to train domestic workers to fill posts in the long term. She added: “The Independent Migration Advisory Committee, which took evidence from a number of NHS trusts and representative bodies from across the UK, recommended against adding nurses to the shortage occupation list.

“Although NHS trusts have been given more than 1,400 Tier 2 certificates of sponsorship for nurses since April this year, over 600 of the places allocated to them in April and May this year were returned unused.”