Jeremy Corbyn has headed to Scotland for his first post-conference visit. It is here that many of Corbyn's supporters are most confident that he can improve Labour's standing (the party has just one Scottish MP and is forecast to endure another landslide defeat to the SNP in next May's Holyrood election). Unlike Ed Miliband, Corbyn is an unambiguous socialist and shares many of the nationalists' distinctive stances: opposition to Trident, tuition fees and austerity (though the SNP's hostility to the latter was largely rhetorical). Corbyn is also an outsider in his party, free of the taint of the Labour establshment and the No campaign.

Unsurprisingly, then, early polls have shown a small swing to Scottish Labour, with another finding that a third of SNP voters are more likely to vote for the party under Corbyn. But those who view the Labour leader as an easy panacea risk much disappointment. On the basis that divided parties never win elections, the SNP has immediately argued that Labour is incapable of defeating the Conservatives, making independence more necessary than ever. To rebut this claim, the party will need to gain significant ground south of the border.

Corbyn failed in his first attempt to make Labour a pro-disarmament party and, owing to the opposition of most of his shadow cabinet and the trade unions (who hold 50 per cent of conference policy votes), he is unlikely to succeed in the future. He has conceded today that the party may enter the Scottish parliamentary election without a clear position - a gift to the SNP. Corbyn's campaign pledge to abolish tuition fees and restore student grants was barely mentioned at the conference, with shadow universities minister Gordon Marsden stating that the party's current position was merely under "review".

But the Labour leader's biggest problem is quite simply that he is a Unionist. For an ever-greater number of Scottish voters, the independence question transcends all others and is the prism through which they view issues such as Trident. Perhaps most significantly, it is those on the far-left, Corbyn's natural audience, who were most disappointed by the referendum result (based on polling by the British Election Study). Whatever else the Labour leader can promise them, he cannot promise to change that outcome. The danger for his party remains that the SNP's hegemony has only just begun.