Britain is facing a sharp round of spending cuts as Prime Minister Liz Truss prepares the country for a new period austerity.

All Whitehall departments are likely to be in the sights of the government as it seeks ways to fund tax cuts.

Levelling Up Secretary Simon Clarke has said the country has lived in a “fool’s paradise” of persistent low growth while expecting taxpayers to continue funding a “very large welfare state”.

He said public spending must be cut to help meet the cost of the government’s £45 billion worth of cuts in taxes which Ms Truss has put at the heart of her “growth” agenda.

The Prime Minister will use the new austerity measures to help justify her fiscal measures to rebellious backbenchers and nervous markets after the Bank of England was forced to spend £65bn propping up the pound which plunged to a record low against the dollar.

Ms Truss and her allies believe the reaction was overdone and will recover when the full details of her plans are revealed in the autumn.

A think tank says plunging gas prices will mean that Chancellor Kwasi Kwarteng’s massive support package for energy bills will  cost £30bn instead of £60bn and that he will balance the books within three years.

As Daily Business reported yesterday, the Centre for Economics and Business Research calculates that the blow from the mini-budget cuts will be far lower than feared.

In the meantime, Ms Truss appears to be unwilling to back big rises in welfare payments and, along with Mr Kwarteng, wants to encourage those on state benefits to seek more work to boost their income.

They will unveil a package of “supply side” measures to accompany a broad sweep of cuts in areas which they view as “too fat” and unproductive.

Mr Clarke said “radical action” was the right course of action.

“My big concern in politics is that western Europe is just living in a fool’s paradise whereby we can be ever less productive relative to our peers, and yet still enjoy a very large welfare state and persist in thinking that the two are somehow compatible over the medium to long term,” he told The Times.

“They’re not. We need to address that precisely because in the end, if we want those strong public services then we are going to have to pay for them.”

However, Ms Truss is facing a battle against an increasingly fractious mood in her party as it heads to its annual conference in Birmingham 33 points behind Labour, according to a YouGov poll.

Some Tory MPs, including one serving cabinet minister, claim Ms Truss – who addresses the party on Wednesday – will be forced to “back down” because the government had lost so much support over its budget.

One said: “We cannot be voting to cap benefits when we’re giving tax cuts to the highest earners.” Another said the actions taken so far threaten higher interest rates which would have the opposite effect of stimulating growth by forcing companies to cut investment.

Some Tory MPs are in talks with Labour about how to overturn the budget, amid warnings that the Conservatives will lose the next election. In particular they want to reverse Ms Truss’s plan to abolish the 45p top rate of tax and possibly the removal of the cap on bankers’ bonuses, moves seen as robbing the poor to pay the rich.

Ms Truss caused further irritation yesterday after rejecting moves to bring forward an independent assessment of the impact of the Budget by the Office for Budget Responsibility. Instead, it will produce a draft report by next Friday ahead of the scheduled forecast on 23 November.

However, any move by backbenchers to overturn the Budget is complicated by parliamentary procedure. The tax cuts will form part of next year’s Finance Bill, while the abolition of the national insurance rise – which has cross-party support – will be put to a vote when MPs return in the autumn.

Mr Clarke, who served as Chief Secretary to the Treasury under Boris Johnson, is expected to play a key role in the new strategy for public finances.

He said spending must “align” with the government’s plan for a low tax, high growth economy.

“It’s very hard to cut taxes if you don’t have the commensurate profile of spending and the supply side reform,” he said.

“If we’re adopting this plan, which I think is exciting and fundamentally addresses the competitiveness issue, the rest of the piece needs to move in tandem.

“We are privileged to deal with very large budgets. My experience . . . is that there is always something you can do to trim the fat.”

Alister Jack, the Scottish secretary, said the Budget tax cuts should not have surprised anyone.

“Over the summer [Truss] was very clear that her strategy was to reduce taxes,” he said in a radio interview.

“To anyone paying any attention to that leadership contest it was plain as day what was going to happen.”

Some Conservatives who either support or are resigned to the strategy believe some major projects will be axed and that billions could be saved by reducing the scope of the HS2 project.

Andrew Bridgen, the Conservative MP for Leicestershire North West and an opponent of the project, told the BBC’s Today programme that he expected it to be ditched.

“It’s going to happen and the government should get on and announce it,” he said.

Lord Wolfson, the chief executive of Next and an influential Tory donor, is among those urging Mr Kwarteng to put HS2 “top of our list” of targets to be cut.