Prime Minister Rishi Sunak and chancellor Jeremy Hunt are exploring a pay offer to try to end the wave of public sector strikes that would backdate next year’s wage award for NHS staff and other key workers.

After weeks of deadlock, Sunak and Hunt are considering giving workers a lump sum by backdating next year’s pay rise, which takes effect from April, probably to the start of January 2023, according to officials briefed on the discussions.

No final decisions have been taken, but the talks reflect fears in Downing Street that the wave of strikes could run on for months, especially if, as expected, public sector workers are asked to endure another year of real-terms pay cuts.

The government is contending with the worst industrial action in decades as workers in the public and private sectors demand higher pay amid the cost of living crisis.

Health secretary Steve Barclay last month floated the idea of a backdated pay award for NHS staff in England but it was never formally tabled to trade unions. But one government insider said: “You could imagine that coming back into play.” Another confirmed that the strategy was being discussed.

Sunak and Hunt face the risk of strikes intensifying when public sector workers are given their first glimpse of what Whitehall departments state they can afford for the pay year starting in April.

Each department was due to submit papers on what they could afford to eight public sector pay review bodies, covering sectors including the NHS, armed forces, police and prison staff, by early February.

Ben Zaranko, economist at the Institute for Fiscal Studies, a think-tank, said that without extra Treasury cash, departments might say they are unable to afford more than a 3 per cent pay rise from April. “That is likely to inflame things,” he added.

Such is the sensitivity of the “affordability” papers that departments have been asked by Downing Street not to publish them yet. Barclay has been reprimanded by MPs for being weeks late in sending in his submission on NHS pay.

With the UK fiscal watchdog forecasting inflation of 5.5 per cent in 2023-24, ministers privately admit that unions are unlikely to respond well to the idea of another real-terms pay cut.

Public sector pay awards for 2022-23 were around 5 per cent. Inflation stood at 10.5 per cent in December.

Although Hunt gave more money to the health and education departments in his Autumn Statement last November, he has told ministers that they will have to fund any pay rises from their existing budgets.

“Any pay deals must be within existing departmental budgets and not fuel inflation further,” said one ally of Hunt. “Current union demands are unaffordable and risk stoking inflation further.”

To try to sweeten the pill, Hunt and Sunak are looking at backdating the April pay award, thereby giving workers a lump sum and addressing, in part, demands by unions that they want ministers to reopen the 2022-23 wage deal.

But the chancellor is adamant that pay must be kept under control and has been briefed by Treasury officials that wage awards in the public sector set a benchmark for settlements in the private sector.

A Treasury memorandum seen by the Financial Times says that public sector pay rises of less than 5 per cent for 2023-24 would have a “low risk” of protracting high private sector pay growth, 6 per cent would worsen inflation, and 7 per cent would “pose a significant risk” and could trigger higher interest rates.

A government spokesman said ministers valued highly public sector workers and remained “open to discussions that will bring an end to the strikes” but added: “We cannot risk high inflation becoming embedded into our economy.”

The spokesman said countries such as France, Spain and Norway had all agreed below-inflation public sector pay settlements for 2022 and 2023, and added: “Finding a fair balance is precisely the reason why we have an independent pay-setting process.”

The Royal College of Nursing and the PCS civil servants’ union, whose members are engaged in strikes, declined to comment.

Both unions have insisted that it is vital that the government addresses their demands for a pay rise in 2022-23.