Rishi Sunak told Cabinet members that the NHS would be “prioritised” amid “difficult decisions” on spending over the coming weeks, Downing Street said.

The Prime Minister and his Chancellor are currently considering tax rises for millions of households and a squeeze on spending to address a black hole of up to £50 billion in the public finances.

According to a Downing Street read-out of Tuesday’s Cabinet meeting, Mr Sunak said that the Government “would always support the NHS and that they would continue to be prioritised as difficult decisions are taken on spending”.

The Cabinet meeting saw the Prime Minister and his top team discuss the NHS ahead of impending fresh pressures this winter.

“He said that in return it was right to look at further ways to improve the service the public receive and that he was confident this could be achieved,” according to Downing Street.

Health spending is one of several major areas that could face further spending constrains, as the Government seeks out ways to restore fiscal credibility in the wake of Liz Truss’s ill-fated mini-budget.

Mr Sunak and Jeremy Hunt are expected to extend a freeze on the thresholds at which people start to pay the different rates of income tax and national insurance, which could result in more people being dragged into higher tax bands as wages increase.

Mr Hunt will set out his plans in the Autumn Statement on November 17 and is considering splitting the burden equally between tax rises and spending cuts.

Public sector workers could face deep real-terms cuts to wages, with The Times reporting that the Treasury is looking at an increase of 2% across the board for 2023-24, at a time when inflation is expected to be well above that threshold.

A Treasury source told the PA news agency that “no decisions have been taken” and the “independent pay review body process takes place next year”.

With BP unveiling profits that doubled to more than £7.1 billion in the three months to September, pressure is continuing to mount for an enhanced windfall tax on oil and gas giants to help fill the Treasury coffers.

Cop26 president Alok Sharma, who was demoted from the Cabinet by Mr Sunak, said: “We need to raise more money from a windfall tax on oil and gas companies and actively encourage them to invest in renewables.”

The warning came as the Resolution Foundation think tank said Mr Sunak and Mr Hunt face an “unpalatable menu” when it comes to rebalancing the nation’s finances.

With a deteriorating economic outlook and the legacy of last prime minister Liz Truss’s disastrous mini-budget as a backdrop, it suggests the Government will need to find at least £40 billion – likely through a combination of tax rises and spending cuts.

The think tank said the Office for Budget Responsibility could predict a recession next year, with GDP forecasts cut by up to 4% by the end of 2024.

Unemployment could also rise by around half a million, the report suggests, with the weaker economic outlook bringing borrowing up by around £20 billion a year by 2026-27.

“The Government has a little over two weeks to finalise its plans to repair its economic credibility and the sustainability of the public finances,” said James Smith, research director at the Resolution Foundation.

“While the recent focus has been on conditions improving post-Trussonomics, the central picture remains one of a weaker growth, higher borrowing costs and expensive tax cuts that have left a fiscal hole of at least £40 billion to fill.”

According to the report, the Government may struggle to meet its fiscal rules of reducing the debt-to-GDP ratio in the medium term and deliver a current-budget balance unless “significant further policy action is taken”.

Among the “menu” of options open to the Chancellor are cuts to investment spending, a move the Resolution Foundation said could save £10 billion but also have a detrimental impact on growth.

The think tank also suggests the Government could try to choose the so-called “austerity option”.

Such a move would require cuts to already-squeezed department budgets.

“With inflation at its highest level for 40 years, Government departments are already seeing their budgets fall in real terms by around £22 billion by 2024-25. It is hard to see how the Treasury could credibly save more than £20 billion by announcing cuts to day-to-day public service spending,” the think tank said.

The Resolution Foundation study suggests the new administration could save £9 billion by choosing not to raise benefits and pensions in line with rising prices next year.

It said any such move would have a “huge” impact on those struggling, with a low-income working family with two children losing around £750 and a pensioner £342.

One option open to the Prime Minister and Chancellor would be to “go full circle” on the mini-budget by reinstating the health and social care levy – a move that would raise £15 billion by 2026-27.

Around £2 billion could also be raised by extending the “stealth” freezes in income tax thresholds by a further year to 2026-27.

Mr Smith said the lesson from history is that public investment projects are likely to face cuts.

“History tells us that this will involve cuts to public investment, which are easy to announce but reduce growth in the longer term,” he said.

“Further austerity for public services is also likely, but there are limits to how big these can credibly be, as public services are already facing cuts of £22 billion thanks to high inflation.

Former Bank of England deputy governor Sir Charlie Bean, speaking at an event launching the Resolution Foundation report, warned that “all the low-hanging fruit” had already been picked on public spending.

“We are at the point where governments have to recognise they can’t do this by efficiency savings,” he said.

Appearing at the same event, Rachel Wolf, who co-authored the 2019 Conservative manifesto, spoke about the stark choices facing the Government on public spending.

She said: “It is almost impossible, at this point, to go back to the central promises of the manifesto.”

Amid questions on spending ahead of November 17, development minister Andrew Mitchell has said that ending a controversial pause on non-essential international aid spending “as soon as possible” would be a “priority”.

On the backbenches, the new minister was a persistent and long-standing opponent of any Government policy that caused cutbacks in aid spending.

In a letter to Sarah Champion, the chairwoman of the International Development Committee, Mr Mitchell said that while the pause would be extended amid Treasury discussions about the autumn statement, ending it “as soon as possible and returning certainty to the FCDO’s Official Development Assistance spend this year and in future years is a priority for my first few weeks as minister for development”.