The Scottish Labour leader, Anas Sarwar, has urged independence supporters to defect from the Scottish National party to “boot the Tories out” of Downing Street, as the first minister, Humza Yousaf, told wavering voters that the cost of living crisis made independence more urgent than ever. As the two leaders made their first major speeches on Monday, in what is expected to be a general election year, both made particular reference to pro-independence voters. The cohort will be essential in the coming campaign as voters previously loyal to the SNP are becoming convinced that Labour can offer more immediate solutions to soaring household bills and crumbling public services. With most recent polling suggesting Sarwar’s revitalised Scottish Labour is close to matching the SNP in Westminster voting intention, he told activists 2024 would be a “momentous” year in which Scotland could “lead the way in booting out these Tories, and electing a UK Labour government”. He added that after “16 years of decline and incompetence” this was “a chance to turn the page on the SNP too”. Speaking at Rutherglen town hall, where Scottish Labour won a “seismic” victory against the SNP in last autumn’s byelection, Sarwar appealed directly to independence supporters – which polling indicates to be about half of voters – telling them: “I don’t care how you voted in the past.” He said: “We may ultimately disagree on the final destination for Scotland, but on this part of the journey, let’s unite to change our country.” But while Sarwar insisted that electing more Scottish Labour MPs would give Scotland “a voice at the heart of the Labour government”, Yousaf said that “what is best for Scotland is likely to be a distant afterthought in the general election contest”. Introducing a series of Scottish government talks at Glasgow University on the economic potential of independence, Yousaf said that for those “who are sympathetic to independence but who are not yet persuaded or who don’t think this is the right time”, his argument was that “independence is urgent”. He added: “It is urgent precisely because the cost of living is top of people’s concerns.” As he highlighted the UK’s productivity gap compared with European neighbours as well as inequalities between London and the rest of the UK, Yousaf said: “It’s impossible to see how any Westminster government, particularly with both main parties committed to Brexit, and with no real economic alternative being presented from Keir Starmer, can change this trend.” In a direct riposte to Sarwar’s appeal to former Yes voters, Yousaf said in a Q&A after the speech that Scotland had a choice whether to elect SNP MPs who had proved they would always stand up for Scotland’s interests or Labour members who were “there to make up their numbers”. Yousaf’s remarks come a day after one of his most senior MPs, Tommy Sheppard, told voters not to abandon the Scottish Nationalists in favour of Labour, arguing that progress towards would be blocked if the SNP lost its Westminster majority in Scotland. Writing for Guardian Opinion on Monday, Liz Lloyd, former chief of staff to previous first minister Nicola Sturgeon, argued that the more Labour is “reliant on latent pro-independence supporters for success”, the harder it becomes for the party to ignore increasing support for separation in the longer term.