Rishi Sunak said he was “happy to talk about pay” with unions as ministers held a series of meetings aimed at ending a wave of industrial unrest in the NHS and on the rail network.

The Prime Minister did not deny suggestions the Government was considering a one-off payment to help NHS staff deal with the soaring cost of living, but insisted any pay settlement would have to be affordable and not further increase inflation.

Health Secretary Steve Barclay was meeting health unions on Monday, including the Royal College of Nursing (RCN), which put the chance of strikes being called off at less than 50%.

Teaching unions were holding talks with Education Secretary Gillian Keegan ahead of announcements this week over whether their members will go on strike.

And rail minister Huw Merriman called in train workers after sustained action crippled services, with only one in five trains running between Tuesday and Saturday.

Setting out the Government’s position, Mr Sunak was asked whether a one-off payment was on the table to resolve the dispute.

The Prime Minister did not deny it, but said he would not comment on “specifics”.

Asked if such a measure would be limited to nurses, the Prime Minister sidestepped the question, telling reporters: “I’m really pleased that union leaders accepted ministers’ invitations to come in today to have discussions across the board and that’s a really positive development.

“And on pay, we’ve always said that the Government is happy to talk about pay demands and pay issues that are anchored in what’s reasonable, what’s responsible, what’s affordable for the country.

“But the most important thing is those talks are happening. And let’s try and sit down and find a way through.”

The Government had previously refused to discuss wages for nurses and other public sector workers, insisting those were matters for the independent pay review bodies but over the weekend Mr Sunak hinted at movement.

Pressed on whether any talks on pay would be about current wage rates or if they would be limited to next year’s settlement, Mr Sunak declined to give further details but said it was a “positive sign” that discussions were happening with the unions.

Health unions have said the pay rises for this year must be renegotiated if strikes planned for later this month are to be averted.

Unless we’re able to have a conversation about this year’s pay award, then, sadly, this isn’t going to resolve the dispute that we currently have with the Government

Patricia Marquis, director for England at the RCN, said on Monday that it feels “unlikely” the nurses’ strikes planned for Wednesday and Thursday next week will be called off.

Asked if it is not even a 50-50 chance at the moment, she told Sky News: “I don’t think it is 50-50, but there is some hope and we maintain that hope.”

She said that while the RCN is “willing to compromise” on its demands, “unless we’re able to have a conversation about this year’s pay award, then, sadly, this isn’t going to resolve the dispute that we currently have with the Government”.

Mr Barclay has suggested a deal may be struck in return for efficiencies but Ms Marquis said this left her feeling “very, very worried”.

She said: “There aren’t enough staff to deliver the care that needs to be delivered and there isn’t enough funding in the NHS.

“Of course, there’s always some sort of efficiencies that can be made but it really does sound like what they’re trying to do is get … the NHS to fund its own pay award and we don’t think that’s possible.”

Shadow health secretary Wes Streeting told BBC Breakfast that RCN chief executive Pat Cullen is “a tough negotiator” who had “shown a degree of reasonableness in the face of Government unreasonableness”.

Elsewhere, Mary Bousted, joint general secretary of the National Education Union (NEU), said “children are being harmed every day by the crisis and the catastrophe of the workforce shortages in our schools”.

Ms Bousted, who said she is “very pleased” to be meeting Ms Keegan on Monday, told BBC Radio 4’s Today programme: “If the Government is serious, they have to do two things – they have to put more money on the table now, and a one-off payment may sound superficially attractive but that brings all sorts of problems with it.

“We want a pay rise which is incorporated into pay in a proper way.

“Secondly, they’ve got to commit to proper negotiations, because this is not just a crisis about the cost of living, although that is a crisis.

“This is a crisis which has been building for 12 years, as we have seen teachers leave our schools and children are left without the specialist teachers they need in order to fulfil their potential.”

She added: “If we take strike action, it’s a last resort to say this cannot continue.”

Sara Gorton, head of health at Unison, said talks about pay are a “major step forward” and the union has “hope” the dispute can be resolved.

Speaking outside the Department of Health and Social Care ahead of her meeting with Mr Barclay, she said: “At the moment, getting in a room and talking about pay is a major step forward. So, let’s see what happens today – we travel in hope.

“We’ll exhaust every possible opportunity to resolve this dispute.”