A controversial target of hiring 5,000 foreign nurses a year for at least 15 years has been cut from a flagship plan to deal with the NHS’s staffing crisis, the Observer understands.

The move will frustrate health chiefs, who are desperate for a clear strategy to reduce NHS staffing pressures, which are expected to worsen.

There are also mounting concerns that new post-Brexit immigration rules could end up making the situation even worse unless the NHS is handed special treatment. The government’s long-awaited plan to tackle shortages included the ambition of recruiting 5,000 nurses a year until 2024 to help relieve short-term pressure. However, it is understood that while the latest version talks about the need for a significant increase in nurses from overseas, the specific figure has been removed.

Senior medics have complained about the government’s failure to solve the health service staffing shortage. Many point to the decision by George Osborne, as chancellor, to stop paying nursing students’ tuition fees and maintenance grants as a key factor in the nursing crisis.

Including the target for overseas would be politically difficult as the government remains committed to a big reduction in net migration. The plan is being drawn up by senior NHS executives led by Baroness Harding, the Conservative peer who chairs the regulator NHS Improvement.

Health experts are still unclear about how new post-Brexit immigration rules will affect the NHS. Proposals released last year that migrants would have to earn at least £30,000 a year would have barred more than 40% of migrant nurses joining the NHS in 2017-18, according to the Nuffield Trust thinktank.

Facebook Twitter Pinterest Dame Professor Donna Kinnair of the Royal College of Nursing described hiring overseas nurses as ‘unsustainable’. Photograph: RCN

It found that 72% of nurses, 70% of scientific, therapeutic and technical staff and 36% of ambulance staff earn less than the required £35,800 threshold for indefinite leave to remain. It said that while occupations with shortages are exempt from the thresholds, such exemptions are temporary.

Its analysis of the new rules warns: “The NHS is in a state of chronic staff shortage due to poor planning and insufficient training numbers over many years. There are 100,000 vacant posts in English trusts alone, although many will be filled by agency workers. The problem is concentrated in nursing and general practice.”

Mark Dayan, policy analyst at the Nuffield Trust thinktank, said: “Even if you take all the actions that we could identify in terms of boosting nurses in training, preventing them from leaving at the same rate, the nursing gap is not going to shrink at all in the next five years without international recruitment.

“We calculated that international recruitment of 5,000 nurses a year would be what it would take to halve the nursing gap, not even eliminate it, by 2023-24. If that doesn’t happen, the sort of shortages we have now will continue. That’s a patient safety issue and the ability of the NHS to move forward and get out of this crisis situation.”

Ditching the figure will place even more pressure on the need to train up British nurses. Dame Donna Kinnair, chief executive and general secretary of the Royal College of Nursing, said: “While it’s beneficial in the short-term, reliance on overseas nurses to plug gaps in England is clearly unsustainable.”

NHS Improvement said: “NHS Improvement and the Department of Health and Social Care are finalising the interim [workforce] plan which should be published shortly.”