The Panelbase poll, commissioned by the SNP, found that 52 per cent of those questioned thought a stronger group of SNP MPs would better stand up for Scotland’s interests at Westminster.
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Just over a quarter (27 per cent) disagreed while a fifth said they did not know.
The poll also found that almost a third (32 per cent) of those who voted No in September’s independence referendum, and 42 per cent of people who voted Labour in 2011, agree that the more SNP MPs are elected the better Scotland’s interests will be protected at Westminster.
Just over four in 10 (43 per cent) of those who voted No and 37 per cent of those who voted Labour in 2011 disagreed.
The poll of 1,018 people also found that 60 per cent agreed that if the SNP holds the balance of power in next year’s general election, the UK Government will have to deliver “substantially more powers to the Scottish Parliament than is currently proposed”, with 20 per cent disagreeing.
Among those who voted No in the referendum just over four in 10 (44 per cent) agree while just under a third (32 per cent) disagree.
The poll found that among Labour voters in 2011, 51 per cent agree and 28 per cent disagree, while among 2011 Lib Dem voters, 44 per cent agree and 33 per cent disagree.
SNP leader and First Minister Nicola Sturgeon welcomed the poll’s findings.
She said: “As this momentous year for Scotland draws to a close and we head into 2015 and the general election, it is extremely encouraging to see more and more people put their trust in the SNP to stand up for Scotland.
“These figures help explain the significant increase in SNP support in the run-up to next year’s general election - which a range of recent polls have shown.
“The fact that a substantial number of No voters and most people who voted Labour in 2011 agree that the more SNP MPs are elected, the better Scotland’s interest will be protected, demonstrates the broad appeal of the SNP campaign.
“Among a range of issues, more powers for Scotland will be at the forefront of many voters’ minds as they head to the ballot box next year.
“And as this poll clearly shows, a majority of three-to-one believe that electing a strong team of SNP MPs is the key to ensuring Scotland achieves the powers we need to succeed - with most No voters and people who voted Labour and Lib Dem in 2011 agreeing with this positive proposition.”
A Scottish Labour spokesman said: “The new leadership team means a fresh start for Scottish Labour and for Scotland. In May Scots face a clear choice - we can send SNP MPs to the House of Commons to protest against the Tories or we can send Scottish Labour MPs to replace the Tories.
“Only a Labour Government will freeze energy prices, tax bankers’ bonuses, increase spending on the NHS and raise the minimum wage.
“Whilst a UK Labour Government will abolish the bedroom tax, the SNP are planning to keep it in a deal to prop up a Tory Government. Scotland deserves better than that.”
• The poll was carried out between December 18 and 23.
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