Rishi Sunak faced devastating losses of more than 1,000 Tory seats in the local elections, while Labour has said the party is on track to win power at the next general election. The prime minister conceded on Friday the English council results were “disappointing”, but faced a scathing verdict from some of his MPs and the first rumblings of a threat to his leadership from allies of Boris Johnson. Keir Starmer, the Labour leader, was buoyed up by winning more than 500 seats, with the party believing its projected vote share puts it on course to take power in 2024 for the first time in 14 years. The BBC’s projected national share of the vote put Labour on 35%, the Conservatives on 26% and the Lib Dems on 20%, while other parties were on 19% – with estimates extrapolated from the England-only local results. On Friday night, Labour was expecting this to be its best local election results since 1997, with an equivalent vote share lead of 8-9% over the Tories. Labour sources said this could result in a majority Starmer government if repeated in a Westminster contest. Labour made significant gains from the Conservatives in the north of England and the Midlands, as well as taking southern councils such as Plymouth, Swindon, Dover and Medway. They celebrated becoming the largest party in local government, which has not happened since the days of Tony Blair in 2002. The party had made surprising successes in Hertsmere, in Hertfordshire, the seat of the deputy prime minister, Oliver Dowden, where the Tories lost overall control of the council. With the dire results rolling in through the course of Friday, the Tories had lost more than 1,000 council seats by the evening, with several councils still to declare. “Make no mistake, we are on course for a Labour majority at the next general election,” Starmer said, having previously urged caution within his shadow team against any complacency about winning. The Liberal Democrats also had a good showing in the south of England against the Tories, winning more than 400 seats, and lifting their hopes of being kingmakers in any hung parliament at the next election. Among their gains were Windsor and Maidenhead, the local council of former prime minister Theresa May, and Stratford-upon-Avon, the seat of the former chancellor Nadhim Zahawi. The Scottish National party also held out the prospect of a hung parliament, with the SNP’s Westminster leader, Stephen Flynn, saying it was “increasingly clear the SNP can hold the balance of power after the next election”. Sunak and his party chairman, Greg Hands, attempted to put a positive spin on the results, insisting there had been “no groundswell” of switching from Conservative to Labour voters. However, some Tory MPs expressed upset at the loss of so many councillors from 2019’s already low base. One of Sunak’s Cabinet Office ministers, Johnny Mercer, an MP in Plymouth where Labour took control of the council, said the party had to improve its response to the cost of living crisis and inflation. At his local count, he said: “We’ve got to do better and we’ve got to learn from tonight.” One Conservative MP described the losses to the Lib Dems and Greens in the south as “a bloodbath”. “Frankly, looking at the results the only way we are going to win is to fight tooth and nail for the north and Midlands, as large chunks of the south are gone,” they said. “And dare I say there seems to be a clear correlation in areas we are holding on and active Tory MPs. Those where the MPs are less than visible, we’re being punished.” Meanwhile, allies of Johnson linked to the Conservative Democratic Organisation (CDO) suggested Sunak should face a confirmatory vote of members and that no one should rule out a comeback for the former prime minister. David Campbell Bannerman, the chair of the CDO, told Times Radio he “blames Rishi because he brought down Boris” and claimed Conservative MPs would act out of “self-preservation” to replace the prime minister. Other Tory MPs were more sceptical, with the former Johnson supporter Michael Fabricant saying: “Part of the whole problem with the Conservatives is not only the cost of living crisis but what happened last year. So if we start to repeat that then we not only will not win the next election, we won’t deserve to.” Johnson is still awaiting the verdict of the privileges committee inquiry into whether he misled parliament over Partygate, and some of Sunak’s supporters blamed “former prime ministers” and the turmoil of the past year for putting voters off the party. Tim Bale, professor of politics at Queen Mary University of London, said the results did “pile on a bit of unexpected pressure” for Sunak, but that this was necessarily limited because of the lack of other credible options for Tories, who did not want yet another leadership election, let alone the return of Johnson. He said: “I think most Conservative MPs have decided that it’s basically Rishi or bust, and they’re going to get behind him. I also think they will take some comfort from the fact that although they have done quite badly, Labour hasn’t done exceptionally well, at least not anything like as well as before the 1997 election.” The polling expert Prof Sir John Curtice also said the “jury is still out” on how much Labour has made progress as a party and said it is not experiencing quite the level of success seen ahead of Blair’s 1997 landslide. However, he said it was on course to be “the largest lead that the Labour party have recorded on our measure since losing power in 2010” and he described the Conservative position as “not far off rock bottom”. Sunak is now likely to face calls from within his party to change direction, although he faces a challenge of addressing a threat from the Lib Dems in the home counties and south-west, and Labour in the north, Midlands and some southern towns and cities. Cracks in Conservative unity already began on Friday with Rehman Chishti, a former leadership contender, criticising Suella Braverman’s rhetoric on immigration. “The comments that we had from the home secretary, the rhetoric that she applies to certain faiths and diverse communities, is damaging to our communities and also it damages the community relations. It feeds into the far right,” he told Sky News.