NHS workers in roles such as blood and transplant services are among nearly 10,000 people being balloted over action that could see them walk off the job as soon as January.
Unite union, which represents 100,000 NHS workers, said voting papers are going out across 36 NHS trusts and organisations in England and Wales.
This is in addition to thousands of other healthcare workers who have already been balloted, the union added.
Unite general secretary Sharon Graham said: "Unite members are now fighting for the very existence of the NHS itself. Crushing staff shortages mean patients' lives are now at risk.
"Twelve years of senseless cuts have driven workers from our most essential public service."
A Department of Health and Social Care spokesperson said: "We are hugely grateful for the hard work of all NHS staff.
"These are challenging times, which is why we accepted the recommendations of the independent NHS Pay Review Body in full and have given over one million NHS workers a pay rise of at least £1,400 this year.
"This is on top of a 3% pay increase last year when public sector pay was frozen and wider government support with the cost of living.
"Industrial action is a matter for unions, and we urge them to carefully consider the potential impacts on patients."
Rail workers, bus drivers, dock workers and waste collectors are among those who have taken strike action in the past few months over pay claims.
In the health service, NHS staff in Scotland have already voted for strike action later this month, and ambulance workers in England are being balloted.
On Wednesday, the Royal College of Nursing said its members in the majority of NHS trusts had backed strike action in their pay dispute.
Health Secretary Steve Barclay said in The Sunday Telegraph that the RCN is demanding a 17.6% pay rise, adding: "It is about three times the average settlement that millions of hard-working people, including many Sunday Telegraph readers, working outside the public sector will typically receive.
"Huge settlements like these would turbocharge inflation when we are endeavouring to keep it under control.
"It will have an adverse impact on people's incomes in the long run."
Meanwhile, the health secretaries in Scotland and Wales have written to Mr Barclay asking for more funding for NHS staff to prevent strike action.
The letter said: "Media reports suggest that the chancellor is considering re-imposing austerity on the people of the UK again, for which there is no mandate, through extensive spending cuts.
"That would be a disaster for our public services, including the NHS, at a time when they need more investment, not less.
"We would therefore implore you to work with us to make the case to the chancellor in advance of his autumn statement for increased funding for the NHS and the devolved governments as a whole, primarily to pay our hard-working NHS staff a fair pay rise in the face of the cost-of-living crisis this winter, and avoid what could be catastrophic industrial action in the NHS."