More than a million NHS workers in England are to be given a 5% pay rise this year and a cash sum for last year, after ministers and unions agreed a new pay deal.

Health Secretary Steve Barclay said he intends to implement the deal, which he called the “final offer”, as he urged the Royal College of Nursing and others holding out to join the majority of health unions in accepting it.

The majority of unions representing staff on the Agenda for Change contract, which includes all NHS workers apart from doctors, dentists and senior managers, voted in favour of the offer.

But health leaders raised concerns over the possibility of further strike action after the deal was not agreed by all unions.

It is the final offer, it’s important that those unions recognise the collective decision

The 14 unions representing staff on the contract have balloted hundreds of thousands of members over the last few weeks.

Unison, GMB, the Chartered Society of Physiotherapy and the Royal College of Midwives were among those who voted to accept the offer, while the Royal College of Nursing (RCN) and Unite voted against it.

The ballot results were reported at an NHS Staff Council meeting on Tuesday, where the majority of unions urged the Government to implement the offer.

The RCN has previously said it will press ahead with a fresh ballot to see if its members want to continue taking industrial action.

And Unite will continue to take action and ask for negotiations to be reopened.

Mr Barclay said: “I’m pleased the NHS Staff Council has voted to accept our pay offer, demonstrating that a majority of NHS staff agree this is a fair and reasonable deal.

“It is now my intention to implement this for all staff on the Agenda for Change contract, and 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.

“We will continue to engage constructively with unions on workforce changes to ensure the NHS is the best place to work for staff, patients and taxpayers.”

He told reporters: “It is the final offer, it’s important that those unions recognise the collective decision.”

“It was negotiated collectively, the RCN were at the negotiating table, indeed (RCN chief) Pat Cullen recommended this deal to her own members.”

Sara Gorton, head of health at the union Unison, who chairs the union group on the NHS Staff Council, 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, 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, said: “Health leaders are concerned that with four trade unions remaining in dispute with the Government over this deal, that the worrying prospect of further industrial action remains.

“Added to that, health leaders are eager for a resolution to be agreed between the Government and BMA, as the last junior doctors strikes saw 196,000 appointments and planned procedures needing to be postponed.

“So, while the NHS Staff Council outcome is very positive news overall, it is not the line in the sand that will allow the NHS and those relying on its care to confidently move on from the threat of future strikes, or from the underlying issues affecting the NHS that led to this activity being felt as necessary in the first place.”

Unite general secretary Sharon Graham said: “Unite’s NHS members have spoken and they rejected the deal.

“Because of this, Unite used its seats on the Staff Council to also vote against it. In fact, we will be escalating strike action.

“The Staff Council vote is not binding on individual unions and therefore the vote will not stop Unite representing the best interests of our members.”

Elsewhere, Mr Barclay will also meet junior doctors from the British Medical Association to discuss the row over pay.

Doctors are campaigning for “full pay restoration”, saying that wages have been cut by more than a quarter since 2008.

But the Government has said that matching the demands of the union is “unaffordable”.

Mr Barclay told reporters that the deal covering Agenda for Change staff showed that the Government was prepared to work with unions and “I hope that we can take that into the discussions with junior doctors”.

“I think what the deal with the Staff Council shows is the willingness of the Government to enter into meaningful, constructive negotiations with trade unions,” he said.