Not since at least 1745, when the Jacobite army reached Derby and seemed poised to take London, has there been such hysteria in England about the Scots. In Covent Garden theatres audiences then sang God Save the King, with its infamous verse – infamous in Scotland anyway – about crushing rebellious Scots.

Read the London-based papers today – and a lot of the Scottish ones too – or listen to David Cameron and Ed Miliband, and it begins to feel as if the Pictish hordes are about to descend from the north again to create havoc and panic. Cameron is not that far behind the Sun’s characterisation of Nicola Sturgeon as the “Scotweiler” with his repeated insistence that the Scottish National party “does not want our country to succeed”. Miliband rules out any deal with an SNP bloc at Westminster, apparently even if it means the Conservatives retaining power.

Not helping either is the condescension implicit in dismissive comments from both Labour and Conservatives describing the mood in Scotland as feverish, beyond reason, mad. My own family, living in Glasgow and elsewhere in the west of Scotland, was once solidly Labour and many of them have shifted to the SNP. There is nothing irrational about it.

My brother John is the biggest surprise. He believed he would go to his grave voting Labour. Brought up in an old working-class district of Glasgow, he was instinctively on the left, joining Labour’s now defunct Young Socialists at age 16. Now 60, he has voted Labour at every election, canvassed for a succession of Labour candidates, and been vocal down the years in denouncing the nationalists – and last September he cast his ballot against independence. But he will vote SNP on Thursday, arguing that modern-day Labour no longer reflects his values, and that the SNP is closer to old Labour. If Labour cannot hang on to him, then they are in big trouble, as the polls suggest, with Scotland poised to send a huge SNP bloc to Westminster.

So what has London – and England or, for that matter, Wales and Northern Ireland – to be worried about? If the Scots are hellbent on going down the road to independence, then so be it. That is their democratic right.

The SNP has changed since the days when its annual party conferences in Perth regularly witnessed the embarrassment of men with replica broadswords shouting about the deeds of William Wallace. While the strains of Caledonia can still be heard at rallies, the party is evolving, cultural nationalism giving way to a left-of-centre, civic nationalism, a process accelerated by the increase in membership over the past six months, many of them former Labour supporters.

The SNP wins regardless of whether Cameron or Miliband becomes prime minister. If the Conservatives emerge as the biggest party, able to put together a coalition with the Liberal Democrats and the Democratic Unionist party, the SNP’s Westminster contingent will engage in guerrilla tactics against austerity cuts and other unpopular Conservative policies. If the SNP enters into some informal arrangement with Miliband, it wins too, better able to wring out concessions.

The SNP strategy for Westminster will be one of attrition. Nationalists looking back for historical models will cite the Irish nationalists at Westminster at the end of the 19th century and the early part of the 20th and how John Redmond in particular succeeded in prising a wide range of powers from Westminster for Irish home rule until the first world war intervened. The SNP will push for concession after concession that will result in more and more powers being devolved to the Scottish parliament – welfare, national insurance, the minimum wage – until one day all that is left is foreign policy, defence, the Queen and the pound. The SNP hope is that, at that point, independence will be almost a fait accompli, the referendum a foregone conclusion.

There are alternative scenarios that do not end with the break-up of the union. If the results are as bad for Labour as the polls suggest, next year’s Scottish parliamentary elections offer Labour an early opportunity for a modest comeback, with proportional representation guaranteeing a presence at Holyrood. And eventually the SNP record will come under proper scrutiny: its spending on the NHS in Scotland is lower than spending on health in England; there have been huge cuts in college places; and council taxes have been frozen. There will be more hard decisions. There is just not the cash available to fulfill all the election promises. So there will be inevitable disappointment, and with it a chance of a revival in Scotland for Labour – and even for the Tories.

The endgame for the SNP remains independence. But polls have not moved in tandem with the SNP surge, at least not yet. Support for independence is up only one point from the 45% in the referendum. There does not seem to be much appetite for a second independence referendum, except in the ranks of the SNP. And the SNP will only push for one when it is certain about the outcome. So will Thursday herald the beginning of the end for the union, or will the Scots settle for more devolution? I suspect the union is over, but it is not yet irrevocable.

If Labour and the Conservatives want to keep the UK intact, demonising the SNP is not the way to go about it. All it does is harden attitudes on both sides of the Tweed, though more so in Scotland, driving even more voters towards the SNP – and eventually independence.