Labour could win support from the SNP if it promised not to re-introduce university tuition fees in Scotland and pledged to make the Living Wage mandatory, a new poll has suggested.

The research, which was carried out by Survation, also suggested a commitment to decommission the Trident nuclear weapons on the Clyde, renationalise Scottish rail services and provide free nursery places for children from the age of 12 months could boost Labour's support.

Survation director of research Patrick Brione said by changing policy Labour could win enough support to restore the party "to first place in Scotland ahead of next year's general election".

While the SNP failed to win September's independence referendum, the party is ahead of Labour in both Holyrood and Westminster polls, and has had a massive surge in membership.

Meanwhile, Labour has lost its leader north of the border after Johann Lamont stood down suddenly, accusing party leaders in London of treating Scotland like a "branch office".

Survation questioned 1,002 people who had previously said they intended to vote SNP for the research, which was commissioned by Progressive Polling.

It found that if Labour pledged to make the Living Wage compulsory, 37% of this group would be more likely to vote Labour, with 6% less likely to support the party, giving a net impact of +30%.

A policy of permanent opposition to university tuition fees in Scotland could have a net impact of +23%, while promising to decommission Trident could increase Labour support by a net score of +20%.

The research found a policy pledge to renationalise Scottish rail services could have the net impact of making +19% of SNP voters more likely to back Labour, while free nursery education for youngsters from the age of one and above could see a net increase in Labour support of +14%.

Mr Brione said: "Our latest Westminster voting intention for Scotland puts the SNP ahead on 46% to Labour's 24%. This means that if Labour could win over the 37% of SNP voters who say that policies such as a mandatory Living Wage would make them more likely to vote Labour, then the Labour Party could enjoy a swing of up to 17 points in the Scottish polls from the SNP - enough to restore Labour to first place in Scotland ahead of next year's general election."

The SNP is already committed to maintaining free university education, with the party also strongly opposed to keeping nuclear weapons in Scotland. New leader Nicola Sturgeon has announced plans to almost double the amount of free childcare youngsters receive if she wins the 2016 Holyrood election.

Neil Foster, head of Progressive Polling, said: "With polls suggesting Labour in Scotland have lost a considerable amount of support to the SNP since the referendum, it is now vital that the party wins back a number of these voters in the coming months ahead of the general election and Scottish Parliamentary elections in 2016.

"This poll of 1,002 SNP voters suggests all is not lost for Labour if the party adopts a number of bold and progressive measures. This Survation poll reveals a significant number of current SNP supporters would be attracted to Labour if they commit to making the minimum wage a Living Wage, bring rail into public ownership, decommissioned Trident, ensured free university fees or offered free childcare after a child is 12 months old.

"This is all fertile ground for Scottish Labour to fight the SNP on and to win back support."