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The All Wales Convention, which was charged with assessing public appetite for a referendum, concluded in November that a referendum was "winnable" but in no way a certainty.
The gap between those who say they would vote yes and no in equivalent BBC/ICM polls over the past three years has grown from seven points in 2008, to 13 points last year, and this year reaches 21 points - a significant margin in favour of a yes vote.
In this latest survey, when people were asked how Wales should be governed, the highest proportion - 40% - said they would like to see an assembly with full law-making powers and some taxation powers.
Another 13% said they wanted the assembly to have full law-making powers but no taxation powers - the only option in a referendum under current legislation.
The desire for Wales to be an independent nation also appears to be waning.
According to the poll, the level of support for an independent Wales outside the UK but within the EU was just 7% with 4% wanting an independent Wales outside both the UK and the EU.
At a total of just 11% of those surveyed, this is the lowest number seeking independence in equivalent ICM/BBC polling.
The poll showed too that 62% of those questioned believe that the assembly government should have most influence over Wales, with 24% saying it should be the UK government in Westminster - similar to last year's figures.
Putting aside your own party preference, who do you most trust to steer Wales towards a strong economic recovery?
Gordon Brown and Carwyn Jones: 47%
David Cameron and Nick Bourne: 24%
Ieuan Wyn Jones and Elfyn Llwyd: 14%
Nick Clegg and Kirsty Williams: 9%
Source: BBC Wales/ICM poll
But when asked which level of government does have most influence over Wales 40% said the UK government in Westminster, while 36% said the Welsh Assembly Government.
That reverses the trend over the past two years, where more people had said they thought the government in Cardiff had more influence over Wales than the government in Westminster.
Two other questions included in this year's poll point to good news for Labour.
In an emphatic response nearly half of those questioned - 47% - said that putting aside their own party preference, they most trusted Gordon Brown and Carwyn Jones to steer Wales towards a strong economic recovery.
Considerably fewer people, around half that number - 24% - said they most trusted the Conservative team of David Cameron and Nick Bourne to bring economic recovery to Wales.
A total of 14% said Plaid Cymru's Ieuan Wyn Jones and Elfyn Llwyd, and 9% put forward Liberal Democrats Nick Clegg and Kirsty Williams.
Again those questioned were asked to put aside their own party preference and decide which one of the four main party leaders in Wales has the qualities to be the best first minister.
The man who in December won the race to become Labour leader and therefore head of the assembly government, Carwyn Jones, was chosen by 38% - a commanding lead over all three other party leaders.
Plaid Cymru leader and Deputy First Minister Ieuan Wyn Jones was chosen by 16%, while 10% named Conservative leader Nick Bourne and Liberal Democrat leader Kirsty Williams.
However around a quarter of those asked to state a preference - 26% - said they didn't know, suggesting that the profile of Welsh party leaders among voters remains low.
Wayne David, Labour MP for Caerphilly, said the poll was "very significant".
"We all know that the economy will be the central concern in the coming election and to have so commanding a lead over the other parties on this issue is very encouraging news for Labour," he said.
"This finding shows that people recognise the steps we have taken to support business and families through these tough times; steps opposed by the Tories.
"Despite the obvious good news for Labour in this poll, there will be no complacency from us and we will continue to fight tooth and nail for every vote right across Wales."
However Welsh Conservative assembly leader Nick Bourne said he did not believe the poll reflected what he had heard on the doorsteps.
"It does demonstrate a trend. I wasn't surprised that the yes vote was ahead," he said.
"I was a bit surprised at the margin, I will be honest."
But he insisted there was still a lot for the 'no' campaign to fight for.
"The [yes] vote has to be won," he said.
"I don't think it's conclusive that just because you have a lead in a poll that you are going to win it. Polls don't decide referendums or elections."
ICM research conducted a total of 1,000 interviews with adults in Wales aged 18-plus by telephone on 19-23 February. Interviews were conducted across Wales and the results have been weighted to the profile of all adults in Wales.
ICM is a member of the British Polling Council and abides by its rules.
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