Imagine a government, eight years in office, pursued by sleaze headlines and with an indifferent record on key issues like education. You might expect such a shop-soiled administration to have some difficulty maintaining support, to be struggling just a bit. Then consider the Scottish National party, which continues to defy political logic.

As the SNP prepares for its annual conference this week, it is currently a mere 35 points ahead of its nearest rival, Labour. It won a sensational landslide victory in the May 2015 general election when it took 95% of Scotland’s Westminster seats. Yet, if the polls are to be believed, its leader Nicola Sturgeon is now even more popular than she was in that “tsunami”, as the general election is called in Scotland.

Not even the transformation of Labour under Jeremy Corbyn has impeded the forward march of Scottish nationalism. In fact it’s becoming clear that the new Labour leader has blown a unique opportunity to turn the tables on the SNP by challenging its claim to be the true inheritors of the social democratic tradition in Scotland.

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Many of those who voted yes in the independence referendum last year weren’t natural nationalists but natural Corbynites. They support anti-austerity economics, non-nuclear defence, public ownership, open borders and compassionate welfare policies. Many actual yes voters attended Corbyn’s packed public meetings during his leadership campaign – I spoke to some of them myself. There has been a bump in Labour’s Scottish membership, but the long-awaited electoral revival remains as elusive as ever.

Some in the nationalist movement were seriously worried when Corbyn first appeared on the scene with an agenda remarkably similar to their own. The SNP has been under a cloud recently in Scotland following the resignation of its business spokeswoman, Michelle Thomson, over revelations about her property speculation. There have been accusations of cronyism in the awarding of state funds to the organisers of the T in the Park pop festival.

The SNP should be wide open to challenge from the left: by its own admission it has failed to address key issues like the educational attainment gap between rich and poor. According to Oxfam, wealth inequality appears on some measures to be increasing faster in Scotland than in the rest of the UK. A raft of prominent yes supporters, like the writer Gerry Hassan, have been attacking the SNP’s very claim to be the party of the left.

But as the new Labour leader’s radical edge has been blunted by his querulous front bench, nationalist anxieties have eased. Corbyn’s commitment to policies like the abolition of tuition fees and the nationalisation of public utilities and the energy companies have either been abandoned altogether or put out “for consultation”.

Facebook Twitter Pinterest ‘According to Oxfam wealth inequality appears, on some measures, to be increasing faster in Scotland than in the rest of the UK.’ Photograph: Murdo MacLeod/The Guardian

Instead of a radical agenda that exposes the skin-deep leftism of the Scottish government, there is a blank space where Corbyn’s election manifesto used to lie. The new Labour leader’s forays north of the border have been an embarrassment to those who believed he represented a departure for Labour in the UK. Waving Irn Bru cans and promising “dour initiatives” is no substitute for coherent policy.

His claim that the Scottish government was responsible for “privatising CalMac, and also were behind the privatisation of ScotRail” was bizarre. The Scottish ferry services are still in state hands, and rail was privatised by the Conservatives in 1993. The Scottish government had no powers to renationalise rail services in Scotland last year when it handed the franchise to the Dutch state-owned company Abellio.

This week Sturgeon is challenging Labour MPs to vote against the Tory government’s fiscal charter in Westminster, claiming that only the SNP are the only party that is seriously committed to opposing George Osborne’s policy of the “permanent budget surplus”.

Corbyn’s equivocation on defence has left Labour in Scotland in an awkward ideological limbo. The SNP leapt on a recent remark by multilateralist Scottish leader Kezia Dugdale, on the BBC, that Labour policy on Trident is “deliberately unclear”. The SNP can now say it is still the only major party that will go into next year’s Holyrood elections opposed to nuclear weapons. The SNP is claiming credit for shadow chancellor John McDonnell’s apparent U-turn on the charter.

And according to the latest polls, the SNP is set for another landslide in Holyrood. According to TNS, the party is even more popular than it was last May. It now has support of 68% of voters aged 16 to 34. The SNP are saying, in terms: tomorrow belongs to us. This is all desperate news for Labour. It lost 40 of its 41 Scottish MPs in the May tsunami, and whoever leads Labour in 2020 will need to recover these seats if the party is to form a UK government; but neither New Labour nor Corbyn Labour has been able to ease the SNP’s grip on Scottish politics.

Unless or until Corbyn manages to have the courage of his convictions and impose his radical agenda on his own party, Labour will continue to hand Scotland to the SNP. A house divided is a house defeated, and it is hard to imagine a party that has ever been as divided against itself as Labour is today – both in Westminster and in Scotland.

The SNP’s dominance is not just because it adopted the “left” policies – like tuition fees – abandoned by Tony Blair. . Many of the Scottish government’s policies – like last week’s privatisation of water services – have been fiercely opposed by the left. Its success has been built on its Scotland-first agenda and an unshakeable party unity, which has prevented subterranean divisions over issues like fracking and the timing of the next independence referendum from breaking the surface calm.

The SNP has been accused of rigging its conference agenda this week to suppress dissenting voices. But the truth is that the vast majority of members seem content to accept whatever their immensely popular leader says about controversial issues. And so far, Scottish voters seem to agree with them.