The SNP's hopes of a post-election deal with Labour have suffered a blow after Douglas Alexander warned his party would not negotiate over Britain's nuclear deterrent.

The shadow foreign secretary refused to rule out a power-sharing agreement with the Nationalists but Nicola Sturgeon's aim of winning major concessions from a minority Labour administration appeared to recede after he said his party would not "trade away" the defence of the UK.

His comments came as a new analysis suggested the SNP was on course to win 45 of Scotland's 59 MPs.

Labour faces being reduced to just 10 seats in Scotland on May 7, a result which would leave the Conservatives as the biggest party at Westminster but without an overall majority, according to the seat-by-seat study by Professor Richard Rose of Strathclyde University.

Paisley and Renfrewshire South MP Mr Alexander repeatedly refused to rule out a deal with the SNP during an appearance on the BBC's Andrew Marr Show, saying he was not "not going to play that game".

He admitted the "polls are tough" for Labour but insisted the party was fighting for a majority.

Splitting the centre left vote in Scotland, he warned, could hand David Cameron a second term in Downing Street.

Asked about Ms Sturgeon's demand to scrap the planned replacement for Trident - which the SNP say would be part of the price for supporting a minority Labour government - he said: "As a prospective foreign secretary in an incoming Labour government the responsibility of defending this country is not something that is the subject of simply trading away interests one way or another.

"Our position on Trident is very clear and I'm not changing it."

Ms Sturgeon has talked up the chances of a "confidence and supply" deal by which the SNP would back Labour budgets in return for major concessions.

The Nationalists would also demand full fiscal autonomy for Scotland and a reversal of spending cuts if it held the balance of power, she has said.

Her comments were echoed by former First Minister Alex Salmond, who told Sky's Murnaghan programme that a formal coalition was "unlikely" but a looser deal that scrapped Britain's nuclear weapons would have "a lot of support" across the UK.

However, Mr Alexander questioned the SNP's appetite for a deal with Labour, saying: "Of course she would affect that's what she wants, although I personally think she may well actually want an in-out referendum on Europe and a Tory government because those would be the most propitious circumstances for further independence in Scotland."

Labour's election co-ordinator dismissed claims by Boots boss Stefano Pessina that an Ed Miliband government would be a "catastrophe" for Britain and played down criticism of the party's campaign strategy by donor John Mills.

Professor Rose predicted the Tories would take under 300 seats and Labour fewer than 280, as the SNP increased their tally from six to 45.

Recent polls have given the Nationalists a 20 point lead or more in Scotland but Jim Murphy, the Scottish Labour leader, said voters would "switch big" to his party in the closing stages of the campaign.

Labour declined to comment on reports suggesting he had ordered his MPs to spend less time at Westminster and more in their constituencies as the election race entered its final 100 days.

Welcoming the new analysis, Stewart Hosie, the SNP's deputy leader, said: "The strong levels of support for the SNP reflect the fact that we always put the interests and welfare of the people of Scotland first.

"Labour are paying the price in Scotland for their toxic alliance with the Tories. "And they show no sign of changing tack. In recent weeks we have seen them vote with the Tories at Westminster for £30bn more austerity cuts, as well as voting in favour of £100bn on Trident renewal, and abstaining on a fracking moratorium. That is exactly why we need a strong team of SNP MPs in a hung Parliament at Westminster to be the force for change."