The people of Scotland are to be offered a historic opportunity to devise a federal future for their country before next year's general election, it emerged on Saturday night, as a shock new poll gave the campaign for independence a narrow lead for the first time.

Amid signs of panic and recrimination among unionist ranks about the prospects of a yes vote on 18 September, the Observer has learned that a devolution announcement designed to halt the nationalist bandwagon is due to be made within days by the anti-independence camp.

The plan, in the event of a no vote, is that people from all parts of Scottish society – rather than just politicians – would be invited to take part in a Scottish conference or convention that would decide on further large-scale transfers of power from London to Holyrood.

A poll by YouGov for the Sunday Times sent shockwaves through the political establishment north and south of the border as it showed the yes camp had 51% to 49% for no, excluding the don't knows. Better Together leader Alistair Darling said: "These polls can and must now serve as a wake-up call to anyone who thought the referendum was a foregone conclusion."

David Cameron was at Balmoral on Saturday night on his annual visit, where growing support for a yes vote was likely to have been raised with the Queen.

With momentum now strongly behind Alex Salmond's push for full-blown independence, the no campaign is desperately searching for ways to seize back the initiative in the last 11 days of campaigning. A win for the yes campaign would represent a stunning turnaround, and unleash the biggest constitutional crisis in the union's 300-year history: it was 14 points behind in polls taken less than a month ago.

However, another poll carried out by Panelbase for Yes Scotland found that no is leading 52% to 48% when undecided voters are excluded.

A senior government minister close to the Better Together campaign said a pledge to set up a new Scottish conference or convention, after a no vote, was imminent. The intention is to demonstrate to the Scottish people that they themselves would be able to "finish the job" of devolution if they reject independence. "Watch this space. You can expect something in the next few days," said the minister.

It is understood that there have been intensive cross-party talks in recent days to finalise the plans. The minister said the conference should be able to complete its work before the May 2015 general election, and in time for the three main Westminster parties to commit to implementing its recommendations in full in the first Queen's speech of a new parliament. Alex Salmond's SNP would be invited to take part.

The move is designed to reassure voters that by rejecting independence they will not be left with the status quo – but that more far-reaching constitutional change and devolution will definitely follow a no vote.

Before the latest poll results were revealed, Rupert Murdoch, the boss of News Corp, said they would be seen as a "black eye" for the British establishment. He said the poll would "shock Britain" and reveal that "everything [is] up for grabs".

"Scottish independence means huge black eye for whole political establishment, especially Cameron and Milliband [sic]," he tweeted.

With the yes campaign in buoyant mood, the no team aims to focus on a message that Scots can have the best of both worlds if they remain in the UK, with more powers, including over tax and their budget, but with the financial security of staying in the UK and EU.

A senior European commission official issued a new warning that an independent Scotland could have to wait five years before getting back into the EU. The high-placed Brussels source said that the internal estimate for the time it would take for Scotland to receive new member status would be around five years, contradicting Salmond's claim that Scotland could negotiate its new membership terms from within the EU.

She said: "It is accepted across the commission that Scotland will need to reapply and every member state will need to agree to them being admitted. There will be a significant wait of at least five to six years. For many Catalans, for example, it is this delay and the disruption to business that is in their mind when they consider independence."

Key figures involved within Better Together have been hinting at a major announcement on further devolution in recent days. The shadow foreign secretary, Douglas Alexander, who represents Paisley and Renfrewshire South, told an audience at Glasgow University on Saturday that the time had arrived to make clear to the Scottish people that real change would follow a no vote.

"One of our challenges in the dozen days ahead is to find new ways of setting out clearly to people just how the process for further devolution following a no vote would work, how civic society will be engaged, and on what sort of a timetable the new powers will be delivered, whichever of the main parties wins the general election." He said the choice was "between greater devolution and irreversible separation". Some critics of Better Together have said it has focused too much on which currency Scotland would use if it voted yes, and too little on how it could change for the better inside the UK.

On Friday, Gordon Brown, the former prime minister, said he wanted to lead a debate in the House of Commons on more devolution as soon as possible after the referendum if Scotland voted no. He said it was time to recognise that it was not just Scotland that would feel the effects of devolution, but England, Wales and Northern Ireland, too.

"The United Kingdom is moving as close to a federal state as is possible in a country where 85% of the population comes from only one of its four parts," he said.

Brown said it had already been agreed that Scotland would have more power to set its own income tax rate, and that there would be more borrowing powers for the Scottish parliament, but he expected more power to set benefit levels and transport policy to be handed to Holyrood.

The former Liberal Democrat leader Sir Menzies Campbell, the MP for North East Fife, who made a similar recommendation for a new Scottish conference in 2012, said it would be "a remarkable opportunity for Scotland as a whole – not just the political parties – to create a relationship with the rest of the UK which to all intents and purposes would be federal".

Campbell said that devolving powers to Scotland, Wales and Northern Ireland would raise questions over whether their MPs should then be able to vote at Westminster on matters where powers had been transferred.

Scotland's deputy first minister, Nicola Sturgeon, said her campaign's canvassing database showed a "significant shift" on the ground. She said: "What we're finding is that as people do make up their minds, they are more likely to be deciding in favour of yes."