“Labour's coming home”, said one of the enthusiastic Corbyn supporters at the Edinburgh Conference Centre last week. “I've been disenfranchised since 2001, but finally this is a Labour Party I feel I can vote for again”

Corbynmania hit Scotland last week, upstaging the coronation of Kezia Dugdale, the new Scottish leader. At Corbyn's Edinburgh gig, described as the hottest ticket at the Festival, the 400 seater auditorium was packed out, leaving “JC”, as he is increasingly known, addressing his customary overspill meetings.

JC is appropriate because listening to the Islington MP is like listening to the many mild-mannered Christians and Quakers who have been around the anti-nuclear movement since my mother and fathers' days.

In Edinburgh he talked of the power of togetherness and solidarity more in the style of a left-wing Anglican vicar rather than a Trotskyite. He was lyrical about the Edinburgh Festival and said that everyone had “a poem or a play in them”.

Corbyn is the rhetorical antithesis of the Respect MP George Galloway. And the truth is that many people like to hear a decent chap with an open neck shirt and pens in his breast pocket talking calmly and sensibly about how to make the world a better and fairer place. They think that's how politicians should talk.

Portraying Corbyn as a marxist militant is one of the many mistakes the UK Labour establishment has made during its leadership election. Calling him a friend of the IRA, an anti-semite, a Militant. A quarter of a million new Labour supporters have signed up because of this man.

Corbyn's anti-austerity economics has very little to do with the revolutionary overthrow of capitalism advocated by the Sparticists who were selling “Worker’s Hammer” outside the EICC. He said he wanted a mixed economy and an industry policy “that everyone accepts as perfectly normal in Germany”.

But here was the most remarkable thing, given the location: JC hardly mentioned Scotland at all. There was nothing in Corbyn's speech in Edinburgh about independence, referendums, fiscal autonomy. He didn't celebrate the Union or “pooling and sharing” and he never mentioned Nicola Sturgeon, let alone Alex Salmond.

And in the Q and A afterwards nor did his audience. I stayed till the very end and there wasn't a single question about the issues that have dominated Scottish politics for at least the last three years.

Which was kind of strange because many of those in attendance were Yes voters – in fact most of those I happened to speak to afterwards were yessers including the authors of the quotes that began this column.

There were lots of No people there as well, of course, but it was as if the independence referendum hadn't happened. It was like entering a benign parallel reality.

There was Hugh Kerr, the former Labour MEP and ardent Yes campaigner chatting away amicably with Simon Pia, the equally strident No campaigner and former special adviser to Wendy Alexander. They don't agree about the constitution or independence, but in Corbyn-world they are both on the same side.

Of course, Corbyn has made clear elsewhere that he is a unionist, doesn't believe in more powers for the Scottish parliament and doesn't think another independence referendum is necessary or advisable. He has hinted at an accommodation with the SNP should he win a general election, but I don't think even he has thought seriously about what he might do if and when he enters Number Ten.

The SNP have been careful not to talk too much about Corbyn, apart from some sympathetic noises at the way he has been denounced as a “cult”, by the Labour right and his supporters as “cybernats” by Alistair Campbell (though that should surely be “Corbynats”). But I’m sure Nicola Sturgeon is beginning to worry about him treading on her patch. She certainly should be.

Until now, Sturgeon has had a near monopoly of anti-austerity politics, apart from the Greens and Plaid, and was a hit in the UK general election leaders’ debates precisely because she was the only one talking about things like unilateral nuclear disarmament. Not perhaps for much longer.

No one in the SNP thought Corbyn could win the Labour leadership. But if the does, then this could open up a new political front on the Left.

Which brings us to Kezia Dugdale who was elected by a modest landslide as the new leader of the Scottish Labour Party, yesterday, along with her deputy Alex Rowley – formerly Gordon Brown’s representative on earth, who has talked at least about autonomy for Scottish Labour.

In her victory speech she remained ultra-cautious – not saying anything remarkable or novel. Only platitudes about her being “a new generation” and that labour was “down but not out. She hasn't come up with any radical ideas for taking Labour forward.

But Dugdale has luck on her side. The Corbyn phenomenon has opened up a new space in Labour politics in which moderate left wing ideas are no longer simply dismissed as far left lunacy. JC may not win, and he's most unlikely to become Prime Minister if he does, but he has changed the culture of the UK Labour Party.

His exemplary personal conduct and his quiet conviction has marginalised the Blairites. The new generation of supporters that has entered Labour as a result of his candidacy will not go away, and they have forced the Labour establishment to take ideas like rail nationalisation and wealth taxes seriously.

Of course, Kezia is going to have to work incredibly hard to dent the authority of Nicola Sturgeon who dominates Scottish politics, and will for many years to come.

But there is an open door here if Kezia Dugdale has the wit to walk through it. There is no one in the Scottish Labour Party now who is going to object to her remaking the party in Scotland as a serious left challenger to the SNP.

She could simply announce that the Scottish Labour Party is an independent force and no one in the UK party would complain. She could even launch that debate on Trident in the Scottish party. Unilateralism is now back on the UK Labour agenda because of Corbynmania.

Dugdale has distanced herself from JC saying she doesn’t want to be “left carping on the sidelines”, but she did make a point of meeting him in Edinburgh, though there was no obvious rapprochement.

But thousands of Labour supporters have turned up to hear Corbyn in Scotland. It would take a real failure of imagination not to seize this opportunity; not to lure these people into the Scottish Labour Party.

Of course, imagination is not a quality that has been present in abundance in the Scottish Labour Party recently. And some things never change. Their only Scottish MP, Ian Murray, announced yesterday that he couldn’t promise to be shadow Scottish secretary under Corbyn.

The sectarian tendency is alive and well in the Scottish Labour Party. Kezia Dugdale is going to have to bang a lot of heads together if she is going to make Labour, not just a has been political party, but a potential government of Scotland.