In a round of interviews, the prime minister showed little sympathy for the pain that high interest rates could inflict on mortgage holders, critics said.LONDON — For Prime Minister Liz Truss, it was a chance to steady the waters after days of turmoil in the financial markets over her new fiscal plan: eight rapid-fire interviews with local BBC radio stations from Leeds to Nottingham.By the time Ms. Truss signed off from the last one on Thursday morning, her political woes had multiplied, leaving her new government in a state of disarray almost without precedent in recent British politics.She was, critics said, robotic in defending a tax-cut plan that had been eviscerated by the markets, and showed little sympathy for the pain that high interest rates could inflict on mortgage holders. One host described her as a “reverse Robin Hood.” A listener on another station asked, “Are you ashamed of what you’ve done?”Barely three weeks into her job, Ms. Truss has suffered a dizzying loss of public support. Her Conservative Party now trails the opposition Labour Party by 33 percentage points, according to a new poll by the market research firm YouGov. That is the largest Labour lead since Tony Blair’s early days as prime minister in 1998, and the kind of gap that usually results in a landslide election defeat.Her plunging poll numbers have badly damaged Ms. Truss’s standing in her party, which is gathering on Sunday in Birmingham for what promises to be an anxious annual conference. Some speak openly of the party ousting her before the next election, though the mechanics for doing that remain complicated.“This is by far the biggest and swiftest hit to a party’s opinion poll rating that British politics has ever seen,” said Tim Bale, a professor of politics at Queen Mary University of London. “For Tory MPs, this is like realizing on your wedding night that you’ve made a truly terrible mistake.”Matthew Goodwin, a politics professor at Kent University and an expert on the Tory Party, said, “I can’t think in my lifetime of any British prime minister who has mismanaged her first few weeks in office like Liz Truss.”What makes Ms. Truss’s predicament so difficult is that none of the escape hatches are appealing. Reversing some of her tax cuts — particularly the one for the top income bracket of people earning more than 150,000 pounds, or about $164,000, a year — would mollify the markets and probably some voters.Tax cuts announced last week by Kwasi Kwarteng, Britain’s chancellor of the Exchequer, threw the markets into turmoil.Clodagh Kilcoyne/ReutersBut it would be a heavy psychological blow for a leader who ran her campaign, and has built her government, on the conviction that tax cuts and supply-side policies will reignite growth. Giving that up, Professor Bale said, would vitiate the ideological rationale of her government and potentially turn her into a lame-duck leader until the next election, which she will have to call by early 2025.Sticking to her guns, which has been Ms. Truss’s response so far, leaves open the chance that Britain’s economy will pick up by the time she faces voters. But the stubborn threat of inflation all but guarantees that the Bank of England, Britain’s central bank, will keep raising interest rates. That will hurt people who need to refinance home mortgages and likely throw the broader economy into a recession.More on Politics in BritainPrime Minister Liz Truss was chosen by a divided British Conservative Party to lead a country facing the gravest economic crisis in a generation.A Domestic Push: After a period of mourning for the death of Queen Elizabeth II, the new government led by Ms. Truss began to work in earnest, announcing several initiatives to address Britain’s economic and social problems.A Turn Toward Thatcherism: Ms. Truss bet on a heavy dose of tax cuts, deregulation and free-market economics to reignite growth. The negative reaction from financial markets underscored the extent of the gamble.Seizing the Moment: Accusing Ms. Truss of losing control of Britain’s economy, the leader of the opposition Labour Party, Keir Starmer, staked his claim as the guardian of sound fiscal policy.Energy Policies: The British government said it would freeze electric and gas bills for households and cut energy costs for companies in an effort to mitigate the effects of Russia’s restriction of gas supplies to Europe.When she was asked by BBC Radio Stoke about her fiscal plan’s impact on the housing market, Ms. Truss paused before saying, “Interest rates are a matter for the independent Bank of England.” She added that “interest rates have been rising around the world” and blamed much of the crisis on Russia’s war in Ukraine.For the last few days, the bank has actually helped Ms. Truss by intervening in the market to buy British government bonds. That brought down interest rates and strengthened the pound, which had tumbled to its lowest level against the dollar since 1985. On Friday, the pound traded up to $1.11.But the intervention, which was driven by fears of the damage done to British pension funds by the turbulent market, has put the Bank of England in an awkward position, economists said. It runs counter to the bank’s monetary policy of raising interest rates to cool inflationary pressures.“The bank has had to reverse course on its objectives practically overnight,” said Eswar Prasad, a professor of economics at Cornell University. “It looks like the bank is being forced to clean up the adverse consequences of the U.K. Treasury’s actions.”“This could have some longer-term implications for the bank’s independence, credibility, and effectiveness,” Professor Prasad continued. “That really hampers it in its ability to fulfill its objectives.”Once the Bank of England completes its bond-buying program on Oct. 14, economists said they expected it to revert to its tighter monetary policy, which would suggest another increase in interest rates at its November meeting. The only government action that could forestall, or even moderate a sharp spike in rates, economists said, would be if the government reversed one of more of its tax cuts.“Absent that U-turn, the bank is going to have to raise interest rates a lot,” said Adam S. Posen, who served on the Bank of England’s monetary policy committee. He said the bank needed to curb both the inflation from an expansionary fiscal budget and the additional inflation caused by a devalued pound.Once the Bank of England completes its bond buying program, economists expect it to revert to its tighter monetary policy by possibly raising interest rates at its November meeting.Hannah Mckay/ReutersBeyond the tug-of-war between fiscal and monetary policy, critics say Ms. Truss faces a more elemental problem: her chancellor of the Exchequer, Kwasi Kwarteng, has lost the faith of the markets in his economic stewardship.That is partly because when Mr. Kwarteng announced the tax cuts last week, he did not submit the package to the scrutiny that a government budget normally receives. That fed fears that the tax cuts were “unfunded,” meaning that they would not be matched with cuts in spending and so would require massive borrowing.On Friday, Mr. Kwarteng and Ms. Truss met at Downing Street with officials from the government’s forecasting agency, the Office of Budget Responsibility — a move designed to signal they now welcomed the scrutiny. The office will submit its projections for the cost of the fiscal program and its effect on Britain’s growth on Oct. 7, but the government will not publish the numbers until Nov. 23.For Ms. Truss, the political fallout from her program’s botched rollout has been profound. Political analysts point out that she won the support of only a third of Conservative Party lawmakers in the first stage of the leadership contest. Now, the collapsing polls have left the lawmakers angry, fearful, and divided.Unless the trends are reversed, many of the party’s members in Parliament will be swept out of their seats in the next election, particularly in the “red wall” districts of the Midlands and the North, where Ms. Truss’s predecessor, Boris Johnson, lured traditional Labour voters to switch to the Tories with his promise to “Get Brexit done.”That realignment of British politics is in jeopardy. Professor Goodwin, of the University of Kent, said these voters did not want Ms. Truss’s low-tax, neoliberal economic policies. Adding to the alienation, he said, she was determined to relax immigration laws, another core issue for working-class voters.“We’re seeing the complete implosion of the Conservative vote,” Professor Goodwin said. “They’re losing middle-class voters who are alienated by Brexit, and working-class voters who are alienated by their economic policy.”For all the hand-wringing, it is not immediately clear what the Tories can do about it. Three months after evicting Mr. Johnson from Downing Street, few people want to go through with another protracted, divisive leadership contest.Professor Bale said another option would be for the party to settle on a consensus alternative to Ms. Truss and then pressure her to step down, so the new leader could be crowned without any delay. The problem with this scenario, he said, is a lack of obvious candidates to step into the role of the party’s savior. More