Humza Yousaf has quelled a rebellion by Scottish National party MPs by agreeing to a compromise with his critics over his independence strategy. The party’s annual conference in Aberdeen decided that if the SNP wins a majority of Scotland’s Westminster seats at the general election, it will have the mandate to negotiate independence with the UK government. After a rebellion that intensified after Labour’s byelection victory in Rutherglen and Hamilton West, the SNP leader dropped his original proposal, set out in June, that the party only needed to win more seats than the next largest Scottish party to win that mandate. He and Stephen Flynn, the SNP’s Westminster leader, took the sting out of the revolt by adopting an amendment tabled by seven senior MPs and several constituency parties that sets a higher target, that the SNP wins at least 29 of Scotland’s 57 Commons seats. Yousaf said “line one” of the SNP’s manifesto would read: “Vote SNP for Scotland to become an independent country.” He said: “We’ve got a Westminster roadblock: if they’re denying us a referendum, let’s use the next general election to put independence front and centre.” In a clear acceptance of criticism that voters were far more anxious about the cost of living than independence, Yousaf said this decision would draw a line on debate about the process of independence and instead allow the SNP more time to argue about the case for it. Flynn said this clarity meant the SNP was now free to show voters there was an “inextricable link” between independence and solving the cost of living crisis. Energy bills, food prices and mortgages were all higher due to Westminster incompetence, he said. “The message could not be clearer,” he told delegates. That new position, the party’s third in as many years, has already been rejected by the pro-UK parties, who say general elections are not votes on single issues. Repeated opinion polls show there is no majority for independence, further invalidating that proposition, they add. Since the constitution is reserved to Westminster – a stance endorsed by the supreme court last year – anti-independence parties also argue that one small party cannot dictate policy on the future of the UK. Opinion polls suggest Scottish voters continue to downplay the importance of independence. A Panelbase poll for the Sunday Times found only 13% of voters agreed that the SNP winning a majority of seats was a mandate, and only 15% supported the “most seats” proposal. The conference vote also killed off Nicola Sturgeon’s controversial proposal last year that the next general election would become a de facto referendum, triggering immediate talks on separation, if the SNP won a majority of all the votes cast. However, the new multifaceted policy does not specify what a majority of seats at the general election would immediately lead to. It said an SNP majority would empower the Scottish government “to begin immediate negotiations [to] give democratic effect to Scotland becoming an independent country”. That could be talks on the UK approving an independence referendum or the UK passing on the powers to stage a referendum to Holyrood. At the same time, the SNP should campaign for more powers for the Scottish parliament and even consider making the next Holyrood elections a de facto referendum. There would also be another constitutional convention. Joanna Cherry, the rebel SNP backbencher who was openly critical of many of Sturgeon’s key policies, implied that Alex Salmond’s fringe nationalist party Alba could be involved in that constitutional convention. “The voices of all minorities” should be heard, she said. One of the sole voices in favour of Sturgeon’s proposal came from Pete Wishart, the SNP’s longest-serving MP, who said that winning a clear majority of voters would be a democratic and credible mandate. “Our one job is to deliver a result that demonstrates the majority of the people of Scotland want to become an independent nation,” he said.