David Cameron and his cabinet will meet in Aberdeen on Monday while Alex Salmond and the Scottish cabinet, whether by coincidence or design, will gather nearby. But it is not in Aberdeen that the future of Scotland – and the United Kingdom – will be decided.

Nor will it be around dining-tables in Edinburgh's well-to-do New Town. Nor the picturesque crofting communities of the Hebrides and Highlands or the small border towns. The frontline in the battle for Scotland is Glasgow, in its long-neglected and poverty-stricken housing schemes. It is there that the 18 September referendum will be won and lost, determined by just how disenchanted voters are with Labour, by people with little to lose, attracted by vague promises that somehow it will all be better in an independent Scotland.

In Glasgow's East End, which has some of the worst statistics in western Europe for child poverty, health, crime, alcohol and drug abuse, there is a widespread fear of Conservatives being re-elected at Westminster next year. "We'll be crucified if the Tories get back in," said a Labour supporter intent on voting for independence.

If the referendum were held today, polls suggest that Scots would vote overwhelmingly against independence. ICM in Scotland on Sunday put support for the no campaign up five points to 49%, with the yes campaign stuck on 37% and those undecided down five points to 14%.

Blair McDougall, director of the Better Together campaign, naturally welcomed the findings. "It is encouraging that undecideds, the group of Scots who are key to this referendum, are overwhelmingly moving in favour of Scotland remaining a strong and proud part of the UK."

Better Together director Blair McDougall. Photograph: David Cheskin/PA

But he should not take too much heart. Other polls have more broadly shown support for the yes camp creeping up over the past few months. Labour politicians, scarred by 2011 when Alex Salmond came from behind to win the Scottish parliament, warn the result will in fact be closer than many suspect.

Although I was born in Glasgow, educated at Glasgow University and worked for both the Herald and the Scotsman, I come fresh to the conversation, after working in the US for the Guardian for the past seven years.

One of the pleasant surprises on arriving back is the vigour of the debate, even with the vote still seven months away, energised especially by the chancellor George Osborne's warning that Scotland will not keep the pound and the European commission president Manuel Barroso's threat that automatic membership of the European Union would be near impossible.

My own family, still living in Glasgow, whom I had expected to be voting no after backing Labour decade after decade are among the don't knows, leaning towards independence, with a nephew already decided in favour.

Another surprise comes from my contemporaries at university, who in our student days were all well to the left and viewed the Scottish National party (SNP) with contempt as the "Tartan Tories". One of those friends, John Henry, a retired history teacher, has only ever voted Labour or Communist but will vote for independence.

In his view, the SNP has moved to become a more progressive, left-of-centre party. "We don't want to be served up any longer with a Tory government or a Labour government that behaves like the Tories," he said. He especially did not like the way the currency warnings were delivered. "The way the three main parties marched in lockstep was quite shocking and we don't like being hectored," he said.

Henry is puzzled that Cameron opposes independence, given it would result in the removal of a large bloc of Labour MPs from Westminster. The only explanation he can come up with is that Cameron is worried about his legacy. "Cameron is wetting himself that he will go down in history as the prime minister who allowed the UK to fracture."

Labour worries about two kinds of voter. Those like Henry who came from the working class, went to university and on into the professions and are now thoroughly disillusioned with Labour. The other, bigger worry, though, is among the disenchanted still living in deprived areas in Dundee, Edinburgh and pockets elsewhere in Lothian and Lanarkshire, but primarily in Glasgow.

Around Duke Street, in the heart of Glasgow's East End, there are a few signs of gentrification. The old tenements have been sandblasted, students are moving in, attracted by cheaper accommodation, and some private houses have been added to the mix.

Shoppers queue for the bus on Duke Street in 2008. Photograph: Murdo Macleod for the Guardian

But there are still the two Rangers' pubs, the Louden and the Bristol, garishly painted in red, white and blue, with the Bristol defiantly flying the union flag. And the social statistics remain abysmal: average life expectancy at birth for men is 68.1 years – five years lower than the Scottish average.

The Labour MP for the area, Willie Bain, out canvassing against independence last week, despairs at the poverty – recent figures showed unemployment rising in the area, in contrast with drops elsewhere – but he argues the problems are best tackled by keeping Scotland part of the UK. His pitch on the doorsteps is one of working-class solidarity, the argument Labour has deployed for decades: working-class people in Glasgow have much in common with their counterparts in Newcastle, Liverpool and Manchester.

The response was mixed. Joseph Gardiner, 44, who has worked in call centres but is unemployed, opened the door to Bain but refused to take his newsletter. He had voted Labour in the past but is now an SNP supporter intent on voting for independence. He said he did not feel intimidated by the warnings from Osborne and Barroso. "I believe the no campaign is based on disinformation, based on fear. Trying to intimidate and scare us. That we can't survive without England. That we can't do it on our own," Gardiner said.

One of Scotland's leading pollsters, John Curtice, professor of politics at Strathclyde University, said Glasgow would be pivotal. The SNP had scored some notable election victories in the East End. "Given we know that voters living in deprived areas such as the East End are somewhat likelier to vote for independence, if the yes campaign does not win the East End of Glasgow, it will not win Scotland as a whole," he said.

He pointed to a slight shift towards the yes campaign over the past couple of months. "Whereas during the autumn the yes side was averaging 38% in the polls, once the don't knows were stripped out, since Christmas they have been running at 42%," Curtice said. "After many months of failing to make any ground at all, the yes side have finally made some progress. The shift may not have been massive and they are still well behind, but the winning post is at least now within their sights for the first time."

Mercifully, the campaign is not about romantic nationalism. Even though it is the 700th anniversary of Bannockburn – one of the Scottish papers ran a piece this month about a computer-generated 3D reconstruction of the battle at the new visitor centre – sentiment appears to have played little part in the campaign.

Nor has anti-English sentiment. If England conceded a goal in the World Cup, a cheer may go up in Scottish pubs but many Scots these dayswatch the Premier League and identify with English clubs and players.

Another surprise is the make-up of a group of yes campaigners out on a soggy night delivering leaflets round Barmulloch, another of the deprived areas of Glasgow's East End. It was led by an SNP member but, contrary to expectations, the other volunteers were an eclectic mix: a Green, two Labour supporters and a former Liberal Democrat. Also in the mix was Graham Campbell, 47, originally from Jamaica, who arrived in Glasgow a decade ago attracted by its music scene. A socialist, Campbell argues the SNP is more likely to deliver social justice. "I do not believe Westminster can be a vehicle for change. It is corrupt and dysfunctional. It is too weighted to the south-east," he said.

It remains unlikely that the Scots will vote for independence. The biggest danger for the no campaign is if polls in the summer and autumn show Cameron is likely to win in 2015. Even allowing for that, the gap is almost certainly too big for the yes campaign to close.

But Labour needs to do more than rely on worries about the currency to deliver the no vote. It needs something to inspire its supporters again. One proposal under discussion in the Scottish party, apart from promising more devolution, is to mount a crusade to tackle the appalling social deprivation in Glasgow and other pockets round Scotland. It is long overdue.