Labour’s leadership believes Scottish politics has reached a “tipping point” where it can beat the Scottish National party at the next general and Holyrood elections after last week’s dramatic byelection result. Party strategists said the manner of Labour’s victory over the SNP in Rutherglen and Hamilton West confirmed it now holds about 35% of the vote in Scotland, allowing the party to win back more than two dozen SNP Westminster seats next year. Peter Kellner, the former president of the polling firm YouGov, said on Monday that level of support puts Labour in touching distance of winning the next Holyrood election in 2026, allowing it to form a minority government after nearly two decades in opposition. Anas Sarwar, the Scottish Labour leader, told Labour’s annual conference in Liverpool that Rutherglen was “proof that Scotland will lead the way in delivering a UK Labour government”. After being introduced by Michael Shanks, who was elected Scotland’s second Labour MP on Thursday with 58% of the vote and a 20% swing over the SNP, Sarwar told delegates the party “relished” elections after years of being scared by electoral contests. “Now no SNP MP can sit safely, taking their communities for granted as so many have,” he said, in an unusually bullish speech, before characterising the party’s increased support as a tide that would sweep its opponents away. “Labour can now beat the SNP across Scotland,” he said, appealing to former SNP voters, thousands of whom failed to vote for the SNP in Rutherglen, to lend their support to Labour to remove the Conservatives in Westminster. Sarwar believes his party is reaching SNP supporters who are upset and disillusioned by infighting after Nicola Sturgeon quit, the police inquiry into party finances and by her failure to deliver a second independence referendum – and that toppling the Tories is now Labour’s most important goal. Many regarded independence as the “parachute” to escape a Tory-run country, rather than an end in itself, he claimed. “I understand why you are desperate for change,” Sawar told SNP voters in his speech. “I understand why you have wanted to run a million miles away from this morally bankrupt Tory government. But I believe that we can work together to boot them out of Downing Street.” Sarwar’s confidence is based on the narrow margins with which most of the SNP’s 44 MPs hold their seats, with Labour in second place in a high number of those constituencies; once Labour begins polling at around 35%, an increasing number of SNP seats become vulnerable. Labour strategists believe they can win 28 Scottish seats, nearly all from the SNP. Speaking at a Tony Blair Institute fringe event with Kellner on Monday morning, Sarwar hinted that he believed the tipping point had arrived. “I am absolutely clear that Scotland will not be a drag on the ticket,” he said, referring to his expectations that numerous Scottish Labour victories at the general election would propel Keir Starmer into Downing Street. But he also told the event that for Scottish Labour, a UK general election was not an end in itself but a “staging post” to a Labour victory in the 2026 Holyrood elections. “I need to be really upfront about that,” he said.