Humza Yousaf has downplayed the Scottish National party’s prospects of winning a key byelection on Thursday as he and his Labour rival traded insults over cuts to public services. Yousaf, Scotland’s first minister, said he was hopeful the SNP would win the Rutherglen and Hamilton West byelection but said the contest had always been “challenging” and “difficult” for his party. With Labour clear favourites to regain the seat, Yousaf said he had always been clear that the SNP faced a battle to hold it after the sitting MP Margaret Ferrier was found guilty of breaching coronavirus rules by travelling by train and visiting local shops while suspecting she had Covid in 2021. Ferrier’s “reckless and dangerous” actions meant the byelection, being held three days before Labour stages what is expected to be its last national conference before the general election, “was always going to be difficult”, he said. “But I go in hopeful of a good result because we have a fantastic candidate, and we have a really positive message of delivering for the people of Rutherglen and Hamilton West over the years that we’ve been in government,” he said. The seat, on the south-eastern fringes of Glasgow, has changed hands three times between the SNP and Labour since the 2010 general election. After Ferrier won in 2015 she narrowly lost it to Labour in 2017, before retaking it in 2019 with a 5,230-vote (9.7%) majority. Ferrier was expelled from the SNP after being found guilty of breaching Covid regulations. Earlier this year she was suspended as an MP for 30 days, triggering the first recall petition for a Scottish seat. The contest has focused heavily on the cost of living crisis and cuts to public services, with the SNP facing direct attacks from Labour for presiding over lengthening NHS waiting lists, cuts to council budgets and wasteful overspends in major projects, such as two long-overdue CalMac ferries. On Tuesday Anas Sarwar, the Scottish Labour leader, focused on suggestions that Police Scotland could shut at least 30 police stations, including three in Rutherglen and Hamilton West, because of intense budgetary pressures. As Sarwar was talking to reporters outside a police station earmarked for possible closure in Cambuslang, a distressed woman trying to report a stalker came up to discover its public counter was closed. The woman, who did not speak to reporters, told Sarwar she had earlier visited her local station in Blantyre but that was also closed. Sarwar said this was “a very stark example” of the SNP’s incompetence and mismanagement, yet the SNP was considering income tax rises, allowing council tax increases and proposing a congestion charge for Glasgow. “This is an out-of-depth first minister, with an incompetent SNP government that has lost its way at a time when people require fundamental change in our country,” he said. Yousaf retaliated by noting that neighbouring North Lanarkshire council, which is Labour-run, had been forced on Tuesday into reversing its proposal to close 39 libraries, sports centres and community centres. The first minister said that U-turn also put under sharp focus proposals by South Lanarkshire, the council that covers Rutherglen, to significantly raise prices at its facilities. Yousaf said his government was generally facing “extreme” budgetary pressures because of UK government funding decisions and the financial crisis. Yet Police Scotland had had a rise in funding this year, as had North Lanarkshire council. Scottish Labour, he said, had repeatedly abandoned its promises to voters: Sarwar had reversed his opposition to the two-child cap for families on universal credit “when Keir Starmer came up from London to give Anas Sarwar his orders”; Sarwar had also reversed his opposition to Brexit. “The Labour party has continued to flip-flop on a variety of issues,” Yousaf said. “We come in with a really strong record of 16 years of delivery.”