The scale of the SNP surge has been highlighted by a new set of polls which show the party on course to take key constituencies held by Gordon Brown, Alistair Darling and Charles Kennedy.

But the party is likely to fail narrowly in its bid to unseat Scottish Labour leader Jim Murphy in May's General Election, the research by a Tory peer shows.

The swing to the SNP could lead to a "dead heat" between Labour and the Conservatives at Westminster, Lord Ashcroft suggested.

His findings point to a possible Conservative wipeout north of the border in the General Election.

Of eight Scottish seats polled, the largest swing to the SNP was in the Fife seat of former Labour Prime Minister Mr Brown, who along with Mr Darling is standing down in May.

Lord Ashcroft said overall his polling suggested that a 22-point swing to the SNP in Scotland could lead to a draw between Labour and the Tories in their battle for Downing Street.

The SNP's election campaign director Angus Robertson said the figures showed that the rise in SNP support was "reflected every bit as much in areas of Scotland which voted No as well as Yes in the referendum".

Mr Murphy said the findings were bad news for Scottish Labour but "great news" for the Tories.

"David Cameron will be rubbing his hands with glee when he sees these polls, because any seat the SNP take from Scottish Labour makes it more likely the Tories will be the largest party across the UK," he said.

A Scottish Lib Dem spokesman said the polls showed the party was "best placed to stop the SNP in the Highlands and the North East", while the Tories said they highlighted that the party was in a "real fight" in Scotland.

Other seats that would fall to the SNP include those held by Labour MPs Sandra Osborne and Russell Brown and Lib Dem MP Sir Robert Smith.

The polls also suggest a photo-finish in the constituency of Scotland's sole Tory MP David Mundell.

Mr Murphy would hold on to his seat, albeit by a slim margin.

The recently-elected Scottish Labour leader announced at the weekend that he planned to stand again for Westminster in May.

He has pledged to lead his party in Holyrood after the 2016 Scottish Parliament elections.

While the Tories could be left without an MP in Scotland, the Lib Dems could have just one, Orkney and Shetland MP Alistair Carmichael.

Lord Ashcroft said: "As things stand, Labour losses in Scotland could offset their gains from the Tories, leading to something close to a dead heat.

"This, then, is the battle: can the Conservatives fight back against Labour faster than Labour can fight back against the SNP?"

Polling analyst Mike Smithson suggested the SNP was now on course to take 56 of Scotland's 59 seats.

Mr Robertson, meanwhile, said that Lord Ashcroft's findings showed how "strong and attractive" the SNP's message was across Scotland, in areas that voted No to independence as well as those that backed a Yes.

"SNP MPs are there to stand up for Scotland, so we'll make sure those things that most matter to the people of Scotland - jobs, the NHS, education and pensions - are not forgotten in Westminster," Mr Robertson added.

"People want to empower Scotland, and they want to vote positively for a party 100 per cent focused on Scottish interests - and see the SNP as the only party which stands for that."

Mr Murphy said: "There is no gloss that can be put on these polls. This is bad news for Scottish Labour but great news for the Tories.

"It is a simple fact that in every election since before the Second World War the largest party has gone on to form the government. In May's election the biggest party will be either Labour or the Tories.

"This poll makes clear that only Labour is big enough and strong enough to beat the Tories across the UK."

The poll is expected to increase pressure from senior Labour MPs for Ed Miliband to rule out any alliance with SNP at Westminster.

Lord Ashcroft's findings show that the preferred outcome in seven of the eight Scottish polls was a Labour-SNP coalition.

A previous set of 16 Scottish constituency polls released by Lord Ashcroft suggested the SNP was on course to unseat other high-profile MPs including shadow foreign secretary Douglas Alexander, shadow Scottish secretary Margaret Curran and Lib Dem Treasury minister Danny Alexander.

That round of surveys also suggested the SNP was in line to take many of Labour's Glasgow heartlands.