But the party still has a mountain to climb if it is to fulfil Scottish leader Jim Murphy’s declared ambition of winning all the seats it won in 2010.
Polls ever since the referendum have shown Labour trailing badly and, with the election looming ever closer, the fear is that a poor performance by the party in Scotland could scupper Ed Miliband’s chances of getting the keys to Number Ten.
Many people in all parties found it difficult to believe the projections of earlier polls that the SNP could win as many as 50 of the 59 Scottish seats at Westminster, reducing Labour to single figures.
But the seat-by-seat polling by Tory peer Lord Ashcroft, published last week, confirmed that the SNP was indeed gaining crucial ground in many traditional Labour heartlands.
Among those who were forecast to lose their seats were shadow foreign secretary Douglas Alexander, shadow Scottish secretary Margaret Curran and former Scottish deputy leader Anas Sarwar.
Most of the constituencies examined in the Ashcroft poll were ones where the SNP and Labour were involved in a straight fight and where there had been a strong Yes vote in last year’s independence referendum.
None of the 16 constituencies surveyed was in or around the Capital. And although the general trend may well be similar here, the results on the ground could prove significantly different.
Past voting patterns and current political battlelines are generally more complex in Edinburgh than in the places selected by Ashcroft.
Traditionally, the Conservatives and Liberal Democrats have had stronger support in the Capital – and although both parties are in the doldrums, their residual vote and the way their previous supporters choose to vote now could be important factors.
In Edinburgh South, for example, Labour’s Ian Murray managed to hold the seat last time against a determined challenge from the Liberal Democrats. But they do not represent a threat this time. The Conservatives used to hold the seat and have sometimes talked up their chances of retaking it, but it was included in the apparent list of “non-target” constituencies discovered on the party’s website.
The SNP might therefore be seen as the main challenger in 2015, but it starts from a lowly fourth place last time and the referendum saw a 65 per cent No vote.
Edinburgh West – held by Lib Dem Mike Crockart – produced an even bigger 66 per cent No vote. Labour had previously targeted the seat, but with the party concentrating on holding constituencies it already has and the seat also appearing on the Tories’ “non-target” list, the Lib Dems now see the SNP as their main opponents, despite the lack of support for independence.
None of the city constituencies produced a majority Yes vote, so even in Edinburgh East, arguably the SNP’s best chance for winning a seat in the Capital, with a 47 per cent Yes vote, the result cannot be seen as a foregone conclusion.
It suggests that despite the understandable temptation to polarise the election in Scotland as an SNP-Labour or Yes-No battle, with fed-up Labour voters switching to the Nationalists, the real dynamics are more complicated and less predictable.