Of all the tough constituencies in the UK, Gordon Brown had to walk into this one. Tough in the political sense, but above all in the street-fighting sense. Glasgow East wears the weary, pinched look of someone who has nothing in life and expects even less. Here, life expectancy for men is said to be lower than it is on the Gaza Strip. Here, the law of the jungle, not Westminister, rules.

And here, on July 24, in a by-election that may enter the history books, Labour could face its nemesis; a fateful collision of hegemony and happenstance.

Glasgow East is a part of the world that defies exaggeration. Desultory buses head out from the city centre towards some of the worst areas of concentrated poverty in the Western world: Shettleston, Barlanark, Garthamlock, Easterhouse, Parkhead... communities that figure with monotonous regularity both on the charge sheet at Glasgow Sheriff Court and at the top of lists of the most socially deprived wards in Britain. They might as well be called Guantanamo. For many thousands of welfare prisoners on sink estates, marooned by bad housing, violence, addiction, unemployment, ill health and shattered relationships, there is little chance of escape. Even a trip to Barlinnie, Scotland's most notorious prison, keeps them within the constituency boundaries.

In pockets, the jobless rate is up to 50 per cent. Male life expectancy is 63, 14 years below the British average. Fifty per cent have no qualifications; only 7.6 per cent are graduates. The over-60s make up 20 per cent of the population, 46 per cent of the constituency is social housing. Shettleston has the highest percentage of residents on incapacity benefit in the UK.

When Iain Duncan Smith, formerly in the mould of a classic right-wing Tory, came to Easterhouse he underwent something of an epiphany, leading him to create his Centre for Social Justice think-tank.

But if the East End's misery could move Conservative hearts, why did it not work on the ruling Labour politicians? One of the first ironies presented by Glasgow East is that it is a classic Labour rotten borough. One of the most rotten of the rotten, in fact. For generations, its inhabitants have been treated as cannon fodder; their votes taken for granted, their poverty contained but largely untackled. Vote Labour? It's what they do, along with drinking, drug taking, bad diet and Irn-Bru. Why should politicians spend money on people who are going to vote for them anyway? Much better to invest it in marginal seats.

In election after election, Glasgow's poor automatically did what their parents had done, with 60 per cent or more of the vote consistently cast for Labour. Corresponding generations of Labour politicians, both local and national, used such loyalty to secure their positions but singularly failed to reward their people.

One could argue that Labour-controlled planners created the problem in the first place, creating the “deserts with windaes”, as Billy Connolly called them, in the 1960s and 1970s. It was Labour which consistently failed to recognise that these vast dormitories - sans shops, sans transport links, sans anything - were a social disaster. It has always struck me as hugely symbolic of Labour's attitude to Scotland's poor that its health policy has always been to offer methadone to heroin addicts - a cheap, semi-permanent form of control rather than expensive rehabilitation.

Only in the past decade have things changed. New Labour started to help Glasgow East after devolution. Jack McConnell, a former First Minister, is credited with the vision of the new Clyde Gateway, a regeneration scheme that began to head east bearing £1.5 billion of private investment and 10,000 new homes. At Glasgow council, under the diligent and perceptive leader Steven Purcell, in the past five years £70million has been invested in new schools and £50 million in housing and apprenticeships for the young.

Then came the winning of the 2014 Commonwealth Games, a Purcell coup that will be used to help to regenerate the East of the city, bringing affordable housing, parks and sports facilities.

As insiders assert, all this amounts to something. Labour has a really good story to tell in Glasgow East. But there is a note of fear in their voices. For there is now a viable alternative to Labour, ready to snatch the prize. The Scottish National Party is poised on July 24 to steal a Labour birthright from under Gordon Brown's nose.

All that investment, the winning of the Games - why, it was Alex Salmond that did it, wasn't it? All the signs are there that this may happen. On paper, Glasgow East may be the 25th safest constituency in the UK, to lose it would require a 22 per cent swing, but we do not live in politically normal times. The Phi100, an authoritative survey of political experts, predicted on Tuesday that the SNP would win it from Labour. Ladbrokes, too, is offering odds of 8-13 on for a SNP win.

If Labour loses Glasgow East, the fallout will be seismic, far bigger than Crewe & Nantwich, signalling the disintegration of the party's hegemony in Scotland and in the UK as a whole. If the SNP can capture this constituency, new Labour is almost certainly finished both sides of the Border. The roof will fall in on Gordon Brown's Government and the Prime Minister himself will be unlikely to survive.

The final irony, of course, lies within the boundaries of Glasgow East, where the massed poor have perhaps not so much shifted their allegiance from Labour as ceased to have any allegiance at all - other than to Celtic FC. Will their lives change, whoever wins the by-election? Doubtful. Very doubtful. Sitting on the slow bus back to the East End, surrounded by drunks and junkies, the constituents inhale the ever-persistent whiff of broken promises.

Times Recommends

• Paralysed while the Hamas hydra lives
• Wanted: a superhero to save America
• Blind faith in experts fails justice