The Treasury would not put a figure on how much the chancellor and prime minister will need to find in the budget next month but the BBC is told it may need to be at least £50bn.
Multiple sources said the amount of money the government needed to raise through spending cuts and tax rises was also more than just this current “hole” in its finances.
This, they said, was because the government needed some “headroom” beyond just getting their existing debt down in case the economy does not grow as much as expected.
And because spending cuts and tax rises in this budget could reduce future economic growth, and therefore future tax revenues, money would be needed to recover that in future.
While government borrowing costs have fallen somewhat in recent days, officials warned Mr Hunt and Mr Sunak that they remain considerably elevated as global interest rates also rise. For example, the interest rate – or yield – on 10-year UK government debt is just over 10 basis points higher than before the mini-budget..
The PM and chancellor agreed that to ensure the package is credible to financial markets, there must also be a buffer – which means a bigger “repair job” than previously expected.
A Treasury source said: “Markets have calmed somewhat, but the picture is still bleak. Britain is facing an economic crisis with a massive fiscal black hole to fill.
“People should not underestimate the scale of this challenge, or how tough the decisions will have to be. We’ve seen what happens when governments ignore this reality.”
Last month, sterling fell to a record low against the dollar as government borrowing costs rose in the aftermath of then-chancellor Kwasi Kwarteng’s mini-budget.
The financial markets plunged into turmoil when Mr Kwarteng announced major tax cuts without detailing how they would be paid for.
But the cost of government borrowing has since fallen back to the level it was at before the mini-budget. The pound also rallied after Mr Sunak became prime minister, and as the dollar fell.
In Mr Sunak’s first speech as prime minister on Tuesday, he said he would “fix” the mistakes made during his predecessor’s time in office.
The PM said he would place “economic stability and confidence at the heart” of his government’s agenda, and promised to show compassion while making “difficult decisions”.
Mr Hunt, who replaced Mr Kwarteng as chancellor after he was sacked by Ms Truss, has already scrapped almost all the tax cuts announced by his predecessor.
But he still needs to find billions of pounds of savings to keep the UK’s debt under control.
