Anas Sarwar says he is certain he can pull off one of the greatest escape acts of modern British politics. It is 14 days until the Holyrood election, and the polls consistently show Scottish Labour is in a battle simply to come second, never mind win.

Those polls are wrong, Sarwar says, and in two weeks plans to prove it. Claiming to be “more than happy” with his party’s underdog status, the Scottish Labour leader insists the media are too obsessed by polling numbers.

Now that postal voting packs have arrived Labour’s canvassers report that many among the unusually high number of undecided voters in this election are shifting towards Labour, he says.

With his party languishing at about 20% in the polls, hamstrung by Keir Starmer’s repeated policy failures and voter anger over the cost of living crisis, those undecided and swing voters are crucial.

Scottish Labour has spent the largest sum in its history on this campaign, targeting hundreds of thousands of voters with tailored adverts on YouTube, Facebook and Instagram, on focus groups, private polling and on parsing highly sophisticated canvassing data.

“What are you going to say after the election, if the polls were wrong?” he asks rhetorically, during a Guardian interview in Glasgow. “You know there are people in this country who will tell you their views rather than just relying on numbers on a spreadsheet.

“The 800,000 people stuck in an NHS waiting list, the 10,000 kids that are homeless, all those families that have been affected by the drugs death crisis because of SNP failure, that’s the numbers I’m interested in.

“I honestly believe from the conversations we’re having that this election is all to play for. I think people do want to reject the poison of Reform. I think people do want the SNP out. What I’m going to persuade them on is that I’m the only vehicle that can achieve it on 7 May.”

Reform is playing a huge role in this election. A dramatic confrontation during a live TV debate earlier this month with its Scottish leader, the multimillionaire yachtsman Malcolm Offord, shone a light on its polarising and disruptive impact.

Sarwar says Labour is targeting 38 out of Holyrood’s 73 first -ast-the-post constituency seats (with another 56 elected via regional lists) but he is rapidly running out of time.

Many observers, including its allies in the Liberal Democrats, believe Scottish Labour is unlikely to beat the Scottish National party outright on 7 May, so would need support from the Lib Dems and Tories to outvote John Swinney and his allies in the Scottish Greens when Holyrood chooses the next first minister.

With Reform on track to win 10 or more seats, it could play a pivotal role in that vote. Midway through a heated Channel 4 leaders debate, Offord alleged Sarwar had secretly suggested to him they should discuss doing a deal.

Sarwar vehemently denied doing so but Swinney, the SNP leader, leapt on the allegation, since repeated by two other Reform candidates, Graham Simpson and Thomas Kerr. Since that explosive encounter, the SNP has posted attack ads on social media suggesting Labour is poised to do a deal with Reform.

Sarwar says what stung him most was Swinney amplifying those allegations, rather than backing Sarwar up when he attacked Offord’s party for standing candidates urging deportation of Muslim citizens and running racist adverts against him in previous campaigns.

“The idea that those that are race-baiting me, that are spending the money on these adverts, are somehow ones that I’m secretly in cahoots with, is offensive, idiotic, and it actually demonstrates how desperate John Swinney and the SNP are,” Sarwar says.

Swinney had the chance at that moment to show Scotland was “unified against that kind of hate”, Sarwar adds. “But John Swinney didn’t choose to do that. He didn’t choose to be a so-called progressive leader, he didn’t choose to demonstrate he wanted to unify Scotland.

“He chose to use that moment to make a political attack on me. Seriously. I think he needs to look in the mirror.”

Sarwar does not deny that Labour could try to build an anti-SNP alliance at Holyrood after the election, but insists he is now working “flat out” to win outright. “My job is not to talk about hypotheticals. My job is to try and create the result we need to win.”

Relying on Reform votes was always politically very difficult for Sarwar; the conflict with Offord makes it impossible. Labour strategists now believe Reform is much more interested in disruption and instability, and would prefer a fifth successive SNP government.

Given those significant difficulties, Sarwar’s allies are furious that the crisis over Peter Mandelson’s vetting has again shifted attention on to a Labour prime minister’s competence and survival, and again allowed Swinney to weaponise public anger with Westminster.

Sarwar has been building up to this election for more than five years. At the 2024 general election, he pulled off an unlikely and significant victory by winning 34 of Scotland’s 57 Westminster seats – Scottish Labour’s best result since 2010.

After watching that polling support then collapse, he took the career-defining risk earlier this year of calling on Starmer to quit – a gamble intended to reassure furious Labour voters he agreed with them and also to prevent Swinney from turning the Holyrood elections into a referendum on Starmer’s government.

Sarwar denies the Mandelson crisis has yet again knocked Scottish Labour off course. He says his message is simple. “A vote for me and Scottish Labour in this election is not an endorsement of Keir Starmer. It’s about who the first minister is. And it’s not a vote to judge two years of a Labour government, it’s to judge 20 years of an SNP government, and it is not a protest election without consequence, it is about whether we get change here in Scotland.”

His problem is getting Scotland’s voters to agree.