The First Minister issued what amounted to a battle cry, suggesting the SNP would be unstoppable after ousting Labour from its third-safest seat.

If the 22 per cent by-election swing was replicated across Scotland in a general election, it would leave just one of Labour's 39 MPs in place – Tom Clarke in Coatbridge – with casualties including Gordon Brown, the Prime Minister, and Chancellor Alistair Darling.

The scale of the defeat piled further pressure on Mr Brown, who faced demands from Paul Kenny, the leader of the GMB union, and the Labour back-bench critic Graham Stringer, to consider his position.

David Cameron, the leader of the Conservative Party, said the defeat showed the country was desperate for change and challenged Mr Brown to call a general election after the summer. But Mr Brown refused to budge, saying he was "getting on with the job" while again trying to empathise with voters about the soaring cost of bread and eggs.

Simple arithmetic shows that the SNP would have 49 MPs, the Liberal Democrats seven, the Tories one and Labour one if Labour's vote collapsed in a similar manner at a general election. The calculation excludes the Glasgow seat currently held by the Commons Speaker, Michael Martin.

As for what the result would mean if replicated in a Holyrood election, a source close to Mr Salmond said: "We are still doing our calculations, but there is no doubt that the swing last night would wipe out all Labour's constituency MSPs.

"They would receive some list MSPs in compensation for the proportion of their vote … but there is no doubt that we would be by far the largest party, although not necessarily in a majority."

By-elections are unreliable indicators of future governments and success can often be short-lived. Of the four SNP by-election victories prior to the success of John Mason in Glasgow East, all but one failed to hold the seat at the subsequent general election.

However, Mr Salmond yesterday maintained that Glasgow East's voters had been in a "unique" situation. Rather than having a choice between a government and opposition, for the first time they were able to weigh the merits of two parties in power – Labour at Westminster and the SNP at Holyrood. There was also the belief among many Labour loyalists that their party had become "arrogant" and needed to be given a sharp kick, he told The Scotsman.

"We have now demonstrated that there are no safe seats for the Labour party anywhere in Scotland," he said. "They used to say that it was the Tories who could only get one MP in Scotland."

Several other factors also give the Nationalists hope that they are on the cusp of smashing Labour's historic dominance in Scotland – and in particular in Glasgow. They point to the fact that the Glasgow East result was the first recent victory against a Labour government. In 1995 in Perth and Kinross, the Tories were in power at Westminster, as they were during the Govan victories of 1973 and 1988. It was only with the SNP's first by-election victory in 1967 that it defeated a candidate representing a UK Labour government.

Then there is Thursday's turnout. At 42 per cent, it was only six percentage points short of the 48 per cent at the 2005 general election. This gives credence to the argument that electors would vote the same way in the next general election, due by June 2010.

Labour could face an earlier test as Jack McConnell, an MSP and former first minister, will be forced to stand down from his Motherwell and Wishaw seat if his posting as High Commissioner of Malawi is activated next year as expected.

Then there is the promised referendum vote in 2010, a year before the next elections to the Scottish Parliament. Roseanna Cunningham, who achieved the last SNP by- election victory when she took Perth and Kinross in 1995, said the benefits to the party this time were likely to be greater. This would be seen most obviously by an increase in younger supporters and a boost in membership.

Asked what the victory would mean for the SNP's hopes of ending decades of Labour dominance and driving forward its aim of independence, Ms Cunningham said: "What we can take from (the by-election] at an absolute minimum is that scaremongering about independence simply doesn't work. That is the difference from between five or ten years ago. That is another sign you can't simply frighten people away from voting SNP."

Labour's search for a new leader in the Scottish Parliament starts on Monday, following the resignation of Wendy Alexander, and many believe the amateurish attempts to canvass support in a supposedly rock-solid constituency – with imported teenage activists getting lost on a daily basis – showed the absence of a grass-roots organisation.

However, Des Browne, Labour's Scottish Secretary, said it was nonsense to suggest that a by-election result could be used as a guide to future voting intentions across the country. He said voters had wanted to register a protest against high prices caused by world economic conditions, and said Labour was already working to re-establish support in Glasgow. However, he did concede that it was a "significantly bad result".

But he compared Glasgow East to the 1999 Hamilton South by-election, which Labour held by just 556 votes from an SNP charge with a virtually identical swing to Thursday. "I remember the SNP issued a press release, which my local paper carried, saying they were about to sweep me away on the basis of that," he said. "It wasn't replicated at the general election and I have defended that seat twice since then."