Voters are “frustrated and angry” at the Conservative government, a cabinet minister has admitted, as the party comes to terms with the heavy losses it took in Thursday’s local elections. Lucy Frazer, the culture secretary, said on Sunday that this week’s results, in which her party lost more than 1,000 local councillors, reflected concerns among voters about the high cost of living. But she insisted the Tories’ poor performance was a result of the party being in power for 13 years and the war in Ukraine, rather than a reflection on Rishi Sunak as prime minister. “It’’s really important that we listen to people,” Frazer told Sky News. “I know people are frustrated and angry.” She added, however, that the results would not prompt a change of strategy in No 10, saying Sunak needed more time to deliver on the pledges he made at the start of the year. “We need to deliver,” she said. “People need to see that we’re a government that says what it’s going to do and then it delivers it.” Separately, she told the BBC: “I have seen a change in mood of the British people. [It was] very difficult at the beginning of the campaign, but slowly [people are] beginning to give the government and Rishi credit.” Frazer’s defence of Sunak contrasts with the message from some of her party’s MPs and local council leaders, who have urged Downing Street to change tack after Thursday’s losses. John Redwood, the Tory MP and former cabinet minister, called for an emergency tax-cutting budget, while Christopher Chope, another backbench MP, said on Friday: “We need to change direction and make it clear to people what we stand for.” Labour, meanwhile, played up the gains it made in Brexit-voting parts of the country where it lost badly in 2019, which party strategists believe will be key to winning the next general election. Figures published on Sunday by the Observer show that in the most heavily leave-supporting areas, Labour is seven points ahead of where it was two years ago. Wes Streeting, the shadow health secretary, told the BBC on Sunday: “Labour has made gains in places that people didn’t expect us to four years ago. Whether it’s in the south of England, whether it’s in the north of England, right across England in places where we need to win to form a the majority, Labour is winning back support. And we’re confident we can win a majority of the next election.” Despite the party’s claims that it is on course for a majority at the next election, polling experts said Thursday’s results were more consistent with Labour being the largest party in a hung parliament. Robert Ford, a professor of political science at Manchester University, wrote in the Observer: “Labour’s 35% share this year is no better than the party achieved last year, a disappointment for the opposition given its big advance in the opinion polls over the past 12 months. Anxious Labour strategists might have hoped for more.” The results have refocused attention on what smaller parties would do if neither Labour nor the Conservatives win a majority next year. Ed Davey, the Liberal Democrat leader, on Sunday ruled out a coalition with the Conservatives but refused to do the same for Labour. Pressed on whether he could do a deal with Labour, Davey said: “That is a hypothetical question, because we don’t know what’s going to happen after the next election.”