In a statement, the NHS staff council confirmed that a majority of its 14 members had backed the deal - despite opposition from the Royal College of Nursing (RCN) and Unite.

The move could pave the way for an end to strikes in the NHS, which began in December last year.

However, the RCN has indicated that it will reballot its members for a further six months of industrial action, raising the prospect that nursing strikes could last until Christmas.

A separate pay dispute with junior doctor members of the British Medical Association (BMA) is also ongoing.

Health and Social Secretary Steve Barclay said he would implement the deal for all staff on the NHS staff council.

He added: “Where some unions may choose to remain in dispute, we hope their members – many of whom voted to accept this offer – will recognise this as a fair outcome that carries the support of their colleagues and decide it is time to bring industrial action to an end.”

UNISON head of health Sara Gorton, who also chairs the union group on the NHS staff council, said ministers and employers must ensure health workers get their money as soon as possible.

She said: “NHS workers will now want the pay rise they've voted to accept. The hope is that the one-off payment and salary increase will be in June's pay packets.

“But health staff shouldn’t have needed to take action in the first place. Unions made clear to ministers last summer that £1,400 wasn't enough to stop staff leaving the NHS, nor prevent strikes. But the government wouldn't listen.

“Proper pay talks last autumn could have stopped health workers missing out on money they could ill afford to lose. The NHS and patients would also have been spared months of disruption.”

Matthew Taylor, chief executive of the NHS Confederation, urged ministers to release the money for NHS staff as soon as possible and to ensure that local NHS leaders do not have to cover the increased cost from their existing budgets.

“Failure to do this would have an extremely negative impact on patient care at a time when there are still millions of people on waiting lists.

“The government promised previously that there will be no impact on frontline services or to the quality of care as a result of the offer, which must be reflected in the additional funding that now emerges.”

Danny Mortimer, chief executive of NHS Employers, said the decision was “very positive”.

“With four unions having rejected the pay deal individually for their members, we await confirmation of their plans.

“However, all unions, whether they have voted to accept the deal or not, as well as NHS leaders themselves, remain concerned about the impact of the cost of living on their members and colleagues, in addition to feeling worried about the present difficulties facing their patients and communities.

“The impending NHS workforce plan is an opportunity for the government to make clear its commitment to invest in staff numbers and development, and for employers to redouble their efforts to improve workplaces across the NHS.”

Meanwhile, members of the RCN returned to work on Tuesday morning after their latest strike in protest at the pay offer.

London’s Chief Nurse, Jane Clegg, said that staffing in the capital’s hospitals had been “exceptionally low” during the strike.

“Beyond these days of action there is also an ongoing impact – as more pressure is put on NHS staff and some Londoners experience delays in their care.”

And Dr Vin Diwakar, NHS England medical director for national transformation, said there had been disruption to cancer services.