Watching the SNP at their Aberdeen conference this weekend, on the eve of a referendum on independence, I couldn't help thinking how extraordinary it is that this is happening at all.

The party may be 80 years old, but it spent most of that time in obscurity. It was Labour that led the drive to restore the Scottish Parliament in the 1980s. In the early years of Holyrood, the SNP seemed to be going backwards, and many of the measures that are now seen as SNP policies - free higher education, personal care - were actually products of the Labour-led coalition. This is the "free stuff" policy that Labour policy advisers like John McTernan now speak of with contempt.

Labour allowed the SNP to become the party of the NHS, nuclear disarmament and free education, while it has become the party of the benefits cap, immigration controls and weapons of mass destruction. I sometimes have to mentally pinch myself to remember that this is actually the case. But it is. Last month, Labour MPs voted overwhelmingly for the Coalition's arbitrary welfare cap - surely a defining moment in British politics.

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Labour introduced university tuition fees when they promised they would not; they supported the renewal of the Trident missile system; they talk enthusiastically about limiting immigration. Indeed, UK Labour politicians spend most of their time apologising for "getting it wrong" on immigration. About the only party that has a good word to say about migrants - or the European Union - is the Scottish National Party, which, as anyone who has any knowledge of nationalist parties in the rest of Europe knows, is remarkable.

Yet, Labour keep going on about the Tartan Tories and how Alex Salmond is the friend of the rich because he wants to cut corporation tax. I don't know how they expect Scottish voters to believe this when it is so obvious that the Nationalists are to the Left of Labour and have been for 20 years. Both Nicola Sturgeon and Alex Salmond yet again made appeals this weekend to Labour voters to join their social democratic vision of an independent Scotland. Indeed, Nicola Sturgeon made the extraordinary claim that a vote for Yes would actually create a renewed Labour Party. I cannot remember any time when the deputy leader of a party of government has made a conference speech promising to deliver a better opposition.

The rise of the SNP almost precisely mirrors the decline of Labour as a social democratic movement. Scots didn't dislike Tony Blair personally - in fact, there is a lot of evidence that they really rather liked him. But they did not agree with his market reforms in the National Health Service and education, or his restoration of university tuition fees in England. Nor was the Iraq War a great "success" north of the Border - though like all voters in time of war, many Scots supported "our boys" at the front. However, Tony Blair and the Iraq War are now ancient history, and there is a Tory-led government again in Westminster. The Scottish Labour Party assumed that they would ride to favour on the back of David Cameron, but it was not to be.

The SNP landslide victory in 2011 came after the return of the Tories in Westminster, and was again built on the policies that Labour had abandoned - in particular, opposition to university tuition fees. It was reported last week by the Institute for Fiscal Studies that English students will still be paying their massive debts in their fifties and that a large proportion of them will never pay it off. Scottish voters only avoided the restoration of tuition fees by voting SNP in 2011 and they know this perfectly well.

Part of the problem is that Labour still believe that the 2011 SNP landslide was some kind of electoral aberration - a bizarre fluke caused by ex-leader Iain Gray seeking refuge in a Subway sandwich bar. Labour still regard themselves as the real "national" party of Scotland. But it is becoming clear that something very fundamental happened in 2011, because the SNP's lead has remained almost constant ever since.

Last week's Survation poll in the Labour-supporting Daily Record indicated that support for independence had declined marginally, but that the SNP's lead over Labour was if anything increasing. If there were an election tomorrow, the SNP probably would not have an outright majority, but it would be by far the largest party, and would call the shots in any coalition with the Greens or the Scottish Liberal Democrats.

This is one important reason why the Yes Campaign seems to be so buoyant, even though it is still significantly behind Better Together in the referendum race. They think that the continued support for the SNP cannot be accidental and that there are grounds for believing that a late surge, as before the 2011 Holyrood elections, will put them over the winning post.

There may be something in that, though the problem is that most of the support for independence seems to be in working class constituencies right now, rather in the middle-class ones. The Unionists remain confident that middle-class Scotland is both more likely to turn out to vote and more likely to be worried by the scare stories about pensions and economic disruption. In their eagerness to harvest ex-Labour voters, the SNP might be ignoring the non-Labour people who voted for them last time.

Though even middle-class voters must by now be wondering what is happening to the Union. Lord Robertson's astonishing remarks last week about independence unleashing "the forces of darkness" were allowed to pass with only mild head-shaking in the editorials of the Scottish press. But just imagine if any senior nationalist had said in Aberdeen that a No vote would give "the dictators, the annexers, the oppressors their earliest Christmas present of their lives". It would have dominated the Scottish press for days.

The threat of currency chaos has also backfired. People have begun to realise - on both sides of the Border - that the idea of setting up some financial Hadrian's Wall to stop Scots using the pound is just not a reasonable thing to do.

I don't know if enough ex-Labour voters will take up the promise of a better Labour under independence. It is still a huge psychological leap for Scots, who have never thought of themselves as an oppressed nation, to start thinking of independence. But I find it difficult to know what the Scottish voters are thinking, because the UK-dominated press is so unionist that only one voice seems to get a hearing.

My sense is that a new Scotland is being created in the heat of this extraordinary campaign, which has now gripped the imagination of every person living in this small country. I'm taking a couple of weeks away to reflect on it all. Hopefully things will be clearer when I come back. In the meantime - don't touch that dial.