Labour leader Sir Keir Starmer has called for Parliament to be recalled so MPs can abandon last week's mini-budget "before any more damage is done".
The value of the pound dropped to $1.05 on Wednesday, after the Bank of England announced it would buy government debt to stabilise the economy.
The Treasury has said its plans were focused on promoting growth.
Sir Keir said the "government has clearly lost control of the economy" and had to do a U-turn immediately.
"Unlike other situations where it may be a world event, an unexpected event that causes this sort of crisis this is self-inflicted. This was made in Downing Street last Friday.
"And for what? For uncosted tax breaks for those earning hundreds of thousands of pounds."
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Parliament is currently suspended while the two main parties hold their annual conferences. It is due to come back on 11 October.
All the main opposition parties - including Labour, Liberal Democrats, Green Party and Plaid Cymru - have now called for Parliament to be recalled early.
The Conservative Party conference is due to begin on Sunday, with Chancellor Kwasi Kwarteng giving a speech on Monday.
Last week, Mr Kwarteng unveiled the biggest package of tax cuts in 50 years, including scrapping the top rate of income tax and lifting the cap on bankers' bonuses.
The Treasury said the plans would be funded by £72bn of borrowing and there is an expectation this will surge as interest rates rise.
The pound slumped following his statement and later fell to a record low against the dollar after Mr Kwarteng hinted there were more tax cuts to come.
Conservative MP Simon Hoare who supported Liz Truss's defeated Tory leadership rival Rishi Sunak - described Mr Kwarteng's handling of the economy as "inept madness".
Mr Hoare, the chair of the Northern Ireland select committee, tweeted: "These are not circumstances beyond the control of Govt/Treasury. They were authored there.
"This inept madness cannot go on."
Managing the market
On Wednesday the Bank of England announced it would buy government bonds on a temporary basis to help "restore orderly market conditions".
The Bank also signalled it is prepared to ramp up interest rates in response to the falling value of the pound, leading mortgage lenders to pull deals.
But the International Monetary (IMF) fund has criticised the UK's plans for tax cuts, warning the measures were likely to fuel the cost-of-living crisis.
The IMF works to stabilise the global economy and one of its key roles is to act as an early economic warning system.
Tory MP Sir John Redwood, a prominent supporter of Prime Minister Liz Truss, dismissed the IMF's criticisms and urged people to judge the government's financial package as a whole.
"The IMF are coming from the errors of the past which they shared with the world's central banks," he told the BBC.
"They didn't foresee the big inflation which they triggered, they didn't have sensible advice in good time to see off the inflation."
The Treasury said Mr Kwarteng was due to publish his medium-term plan for the economy on 23 November, which would include ensuring that UK debt falls as a share of economic output in the medium term.
On Monday the Treasury sought to calm markets by saying it would publish a plan to tackle debt on 23 November.
The prime minister was initially reluctant to intervene, according to the BBC's political editor Chris Mason.
But he said he had been told reports of a "shouting match" between Ms Truss and the chancellor were "plain wrong".
It said it understood the package aimed to boost growth, but warned that tax cuts could speed up the pace of price rises and increase inflation.