Most health unions accepted an offer of a 5% rise for 2023-24 and a one-off backdated payment for last year, following a 4% rise for 2022-23.

The RCN has rejected the deal.

A source from the Department of Health said the pay offer was final, with Energy Secretary Grant Shapps calling the deal on the table "very generous".

Speaking to the Times, union boss Pat Cullen praised her "courageous" members and urged ministers to reopen talks, starting with an offer of a double-digit pay rise over the two-year period.

The RCN had last year called for a rise of 5% above the RPI inflation rate, which peaked above 14% in October, but no UK nation has offered close to that.

It later called for RCN union members to accept the government deal, but they voted against it by 54% to 46%.

The nursing union will now ballot for further strike action later this month.

In her interview, Ms Cullen said: "Looking back on this pay offer, I may personally have underestimated the members and their sheer determination."

She called on Health Secretary Steve Barclay to reopen negotiations which she said needed to "start off in double figures".

Ministers owe it to nurses "not to push them to have to do another six months of industrial action right up to Christmas", she added.

An RCN spokesperson added: "The negotiations covered two financial years which resulted in a consolidated NHS pay increase of 9%. When our members rejected that, it is clear they expect an offer into double figures."

Nurses in England went on strike for 24 hours on 1 May - it was the first time RCN members walked out of all areas, including intensive care.

They also took industrial action on two other occasions earlier this year, on 6 and 7 February and on 18 and 19 January.

Mr Shapps told Sky News that it was "curious" for Ms Cullen to be asking for a double-digit rise when members had previously been encouraged to accept the smaller offer.

He said he thought it was a "great settlement", adding: "I thought it's terrific that it had been reached.

"It's frankly rather confusing now that having encouraged her members to accept that deal, she seems to now be coming back and saying the opposite."

Asked if it was an "absolutely no" to a double-digit pay rise, he replied: "You've got to balance that with the rest of the public purse and there's a very generous offer now on table... and I think it would be a great way to get this settled."

Speaking ahead of the annual RCN congress in Brighton, Ms Cullen said she was "proud" of RCN members.

She praised their "selflessness" for rejecting the government's pay offer and losing pay on strike days to "stand up for the NHS".

"Nurses believe it's their duty and their responsibility because this government is not listening to them on how to bring it back from the brink and the message to the prime minister is that they are absolutely not going to blink first in these negotiations," she added.

Eleven health unions backed a deal on 2 May, meaning more than a million NHS staff would receive a 5% pay rise.

The deal, which includes nurses in England, also entails a one-off payment of at least £1,655. It means all staff will now receive extra pay.

Some unions rejected the offer, including the RCN and Unite, but it was accepted after a majority was reached. Both unions warned they would continue to pursue strike action.

Asked in the paper why nurses warrant a larger increase than other healthcare workers, she said: "It's not so long ago since the prime minister went on the media and very publicly said nurses are an exception."

"I would totally agree with him... they should be made an exception because they are exceptional people."

A government source said the health secretary's door was open for discussions about how to make the NHS a better place to work and it was getting the money into staff pay packets as soon as possible.

"It is time to move on from industrial actions and work together to deliver for patients," added the health department source.

Nurses in Wales are set to strike this summer after rejecting the Welsh government's latest pay offer.

And in Scotland, union members have accepted an offer worth an average 6.5% for 2023-24.