THE SNP's big referendum push, during which Alex Salmond revealed the date Scots will vote for or against independence, has failed to boost support for the Yes campaign.

The latest poll, published today, shows support for independence fell to 30% last month, down three points compared with February's figure.

Backing for the Union also fell in the latest TNS BMRB survey, dropping one percentage point to 51%, as the number of those unsure how to vote when the nation decides on September 18 next year rose from 15% to 19% over the month.

Although both sides in the referendum race lost support, the findings are likely to come as a bigger disappointment to the Yes camp.

TNS BMRB quizzed 1002 voters from March 20 to April 2 – the period immediately after the First Minister unveiled the date of the referendum.

The announcement, accompanied by a huge fanfare from the SNP and the Yes Scotland pro-independence group, was followed by the Nationalists' spring conference in Inverness, at which the First Minister stepped up efforts to explain what he called "the why of independence".

SNP ministers were also on the front foot over the so-called bedroom tax, promising to reverse the cuts to housing benefit if Scotland were to become independent.

Hopes of a significant poll boost, however, have failed to materialise. At 30%, support for independence is higher than it was during the latter part of last year, but remains well below the post-2007 high of 39%, recorded a year after Mr Salmond became First Minister for the first time.

Support for remaining in the UK fell despite embarrassment for the Scottish Government over a leaked Cabinet briefing paper in which Finance Secretary John Swinney voiced private concerns about the state of the country's economy and the affordability of pensions and unemployment benefits in an independent Scotland.

The pro-UK Better Together group, which obtained the document, claimed it undermined the SNP's economic case for independence and saw the leak as a breakthrough in the campaign. However, the revelations, coupled with the SNP's big push, appear to have combined to increase uncertainty in the minds of voters.

Chris Eynon, of TNS BMRB, said polling had showed little fluctuation this year. He said it was early days for the campaign: "With the potential for voter fatigue a real concern, we are unlikely to see much concerted activity getting under way until the autumn at the earliest. The contest for hearts and minds on Scottish independence has not even begun."

The latest poll put the No camp 21 points ahead, compared with a lead of 19 points the previous month.

Going back to the start of the TNS BMRB series in 2007, the gap was at its widest last October when support for independence lagged by 25 points, and at its closest in mid-2008 and early 2009 when it trailed by just two points.

Today's poll also confirmed the gulf between the views of men and women. Support for independence was 36% among men and 25% among women. Similarly, 47% of men said they would vote No compared with 55% of women. However, women were less likely to have made up their minds, with 21% undecided on how to vote compared with 17% of men.

Those aged 45 to 54 are most likely to support independence, with 41% in favour compared with 42% against. The youngest and oldest voters are among the strongest supporters of staying in the UK. Among 16-to 24-year-olds, 29% said they would vote Yes, compared with 52% voting No. Among the over-65s, 22% said they would vote Yes compared with 60% voting No.

The pollster posed the question that will appear on the ballot paper in next year's referendum: "Should Scotland be an independent country? Yes/No."