By midday on Wednesday, Louise Spencer has £6.80 left in her purse to last until Monday, which works out at £1.36 a day to pay for anything she and her two small children might need. She is confident that she will make the money stretch. It's just a question of careful budgeting.

Frugality is an art she has already perfected. This morning she has done the weekly shop, which came in 67p cheaper than the £20 she had set aside. Providing a week's worth of meals for three people for £6.66 a head is easy once you work out how, she says. The gas and electricity payments for the week have already been made, so she knows the children will be warm. The only thing to fear is the unexpected - a broken pushchair, a request to buy her daughter's class photograph.

Louise, 24, doesn't smoke, drink or take drugs and she very rarely goes out with her friends. She spends pretty much all the money she gets in benefits on her children. She rejects the suggestion that her family might be described as poor. "Oh no," she says firmly. "We get by."

According to the official definition, Louise's family are surviving well below the breadline, and Abigail, five, and her son Sean, three, take their place alongside the 3.9 million children in Britain classified as living in poverty.

Today marks the 10th anniversary of Tony Blair's promise to eradicate child poverty by 2020. In a lecture on his vision for the welfare state, he set out "our historic aim - that ours is the first generation to end child poverty for ever". The government would, he promised, "break the cycle of disadvantage so that children born into poverty are not condemned to social exclusion and deprivation". Gordon Brown echoed the commitment, describing child poverty as "a scar on the soul of Britain".

It was a slick soundbite of a promise, which prompted some scepticism at the time, but money has been spent and over the last 10 years there have been some modest improvements. In 1999 Britain had a higher proportion of children in poverty than any other western European nation. Since then, 600,000 have been lifted above the breadline; we're still bottom, only now we share the ignominy with Italy and Spain. About 30% of children remain beneath the breadline and the recession is likely to increase that number; the government's promise to halve the number of children in poverty by 2010 has been quietly swept under the carpet and no one expects it to be met.

You have to suspect that Blair didn't come to Hartcliffe before he launched the campaign, so complex and entrenched are the problems here. This postwar estate on the outskirts of Bristol, just before the city snaps into countryside, has one of the highest rates of teenage pregnancy in the country, widespread drug use and very high levels of poverty. Since the closure at the start of last recession of the Wills cigarette factory, the largest tobacco plant in Europe, unemployment here has soared.

When Blair made his speech, Louise was already in a cycle of disadvantage, from which she is still fighting to escape. The daughter of a teenage mother who left school without any qualifications, she was shortly to finish her education with only a handful of Es, Fs and Gs at GCSE. Inspired by a school careers session, she had hoped, briefly, to become an archaeologist until teachers stamped on the aspiration, pointing out she didn't have a chance of getting into university. Instead she thought she might become a nursery assistant and began training, but abandoned it when she got pregnant, aged 18. "You do dream about what you're going to do, when you're at school. But life doesn't work out like that," she says with no bitterness.

Ten years of government pledges to tackle social exclusion in places such as Hartcliffe has, as far as Louise can see, resulted in little more than the demolition of the local parade of shops, most of them boarded-up since riots in the 1980s, and the construction in its place of a massive, cavernous Morrisons and a new Iceland. This shopping complex looms large in Louise's life. On Mondays she comes here to the Post Office opposite to pick up £85 in income support. On Tuesdays she comes to get another £51 in tax credits. Burned by the high charges imposed on her overdraft, she no longer has a bank account and deals only in cash. Her daily routine is punctuated by anxious furrowing in her pink wallet, and the careful updating of her weekly personal accounts in Biro on the back of an envelope: £5.50 for TV licence, ticked off; £10 for gas meter, ticked; £5 for electric, ticked; £10 repayment of a loan to the council; £7 repayment of overdraft charges to Lloyds TSB; £5 for her mobile; £5 for nappies; all ticked off.

Shopping at Morrisons doesn't take very long. Louise has a simple formula: don't buy anything that costs more than £1. This week, the budget bananas are finished, and the regular packet costs £1.29, so she doesn't buy bananas. The cheap potatoes are also sold out, so she doesn't buy potatoes. She fills a basket with Morrisons own-brand orange juice, 56p; reduced-sugar jam, 95p; peanut butter, 78p; yoghurt, £1.00; bread, 99p, granulated sugar, 93p; oven chips, 79p; two tins of eight hot dogs at 49p each; one bag of value apples, £1.00. Only the milk, biscuits and the cheese cost more. She ignores the faltering monologue from her son, who has been diagnosed with learning difficulties, just audible from beneath the pram's hood. "Mum, I want flowers. Please buy flowers. I want the Bob the Builder egg. I want High School Musical chocolates . . ."

"It would be nice, on occasion, to buy them something on a whim - treats, cakes and biscuits. But if you do, you know you're going to have to turn the heating off," she says. Her face is pallid, and she has grey patches of exhaustion beneath her eyes.

She crosses the car park to Iceland to find cheaper bananas (brown and verging on rotten), pizza, cheese spread and chicken pies for £1 each.

"This will easily last me until next week, and there'll be stuff left over," she says confidently, although she concedes that things would be better still if she could spare £4 to make a bus trip into the city centre for the weekly Wednesday food handouts by nuns, who usually give her a couple of plastic bags of tins and pasta. Last harvest festival her daughter's school was collecting for the nuns, so she sent in a few tins she had been given by them, and is half-expecting to see them come back full circle and return to her cupboard.

On the walk between the shops and her two-bedroom ground-floor flat, every second person is a very young mother pushing a pram. Louise says Hartcliffe is notorious across Bristol as a "dumping ground for single mums". Poverty in Britain is defined by a relative measure, rather than an absolute one; any household with an income of less than 60% of British median income is classified as in poverty. At the moment, for a single-parent family with two children, the official cut-off line stands at £199 a week, after housing has been paid for; for a two-parent family, it stands at £283.20 a week.

"Everyone is trying their best for their family. Some mothers are growing marijuana in their flats and dealing drugs on the side. They do it because they think it is the only way to give their children a better life," she says, without passing judgment. Other mothers regularly pop into Morrisons to steal stuff they can sell, to supplement their income.

"There are people in a much worse situation than me, people who aren't as organised as I am. They get their money and they spend it willy-nilly and then their children go hungry," she says. When she was still battling with bank charges imposed by Lloyds every time she went overdrawn (which was every week), she would do without meals herself because there wasn't enough food, but life has improved now that she has switched to the Post Office, and is slowly paying off a debt of £600-worth of fines and charges to Lloyds.

Louise is not inclined to blame the government for her difficulties. She is grateful for the money she gets every week and doesn't think her life would be much enhanced by increased payments. "Money can't always make you happy," she says. "I'm not a greedy person. When you've learned to survive on very little, you can't afford to be greedy."

Instead, she has become adept at making do. When she moved into this flat, after her children's father left her, she had almost nothing. Her mum bought her a secondhand sofa for £30, a charity gave her a washing machine (so old that it barely works). Because there's no dryer she has a complicated timetable by which she can ensure clean, dry school clothes for her children for the next two days, spreading out knickers, socks, T-shirts, trousers on every radiator in the flat. Because there's no table, the children eat on the floor and she eats on her lap.

At first sight, the flat gives an impression of profound chaos. Clothes are piled into cardboard boxes in the corner. Belongings are balanced on broken bits of furniture. Saucepans are stacked high on the top of the stove. It's not that she's not house-proud, but being poor gets in the way. There are no cupboards, so everything is shoved into boxes, or spilling out into the open. The children's dolls lie legs poking up into the air on the floor, because buying a toy box has never been the week's most pressing purchase. There was no carpet in the flat, but someone has found her an old strip of blue carpet, secondhand, that doesn't fit into the room, curling into rolls at the walls, and leaving a third of the cold cement floor exposed, so that when her son tumbles off the sofa, he lands on his forehead on the concrete, and a red lump swells up. Louise gathers him up and rocks him, whispering "My boy, my boy" in his ear.

The block has all the usual accoutrements of deprivation - abandoned mattresses in the back garden, a broken chair propping open the door, kicked-in wooden fencing, layers of graffiti. Someone keeps painting "Nigger" on the front door of the people who live in the flat opposite, but the tenants have carefully whitewashed over the graffiti, and now the pink door has two white stripes across the front. Neat, white parking bays have been painted on the asphalt outside the three-storey, redbrick block of flats, but they are all empty because no one here can afford to drive a car. In the park opposite, near the school for children who have been permanently excluded from their secondary schools, Louise finds herself stepping over needles as she brings her children home in the afternoon.

In the same speech, 10 years ago, Blair promised that his government would tackle the fundamental causes of child poverty - structural unemployment, poor education, poor housing, crime and a drugs culture. None of that has been done in Hartcliffe.

As they come into the stairwell, Louise's daughter says: "It stinks in here." At five, she is already angry at her situation in a way that her mother is not. Hungry after school, she says: "I want cake." Louise replies in a voice weary from repetition: "We don't have cake. I don't have money for cake." Later, she makes chips and beans and pizza for supper. She knows that fresh food is important, but you can rely on tinned hot dogs and frozen pies not to go off, so that way nothing is wasted. Once a month when the child benefit payment comes through, she'll buy ingredients to make her own lasagne, or stew, from scratch.

Somehow, popular support for tackling child poverty in Britain has never been won, either by the government or by the legion of charities working in this area. While Live Aid and the campaign to end developing-world debt got hundreds of thousands out into the streets, there has never been much public enthusiasm for pouring money into relieving poverty in our country.

People associate child poverty with distended stomachs in Africa and slum kids in India and find it difficult to engage with the home-grown equivalent, campaigners say. Many still refuse to concede that poverty even exists here, arguing that if children are housed, fed, and have access to free healthcare, they have nothing to complain about. Others have peculiarly outdated conceptions of British poverty, "half Dickensian, half wartime, with images of children in ill-fitting clothes, very far from the reality," says Hilary Fisher, director of the Campaign to End Child Poverty.

Poverty for children in Britain now is more likely to mean not having a winter coat, never having enough money to go on holiday or on school trips, not having the spare pound needed to join subsidised after-school clubs, not being able to afford to go swimming. It isn't about going hungry, but it is likely to involve eating irregularly, cheaply and badly.

The tabloid portrayal of the poor as idle scroungers has done a lot to weaken public sympathy for the cause, even though new data shows that the majority of children living in poverty have at least one parent who is working, but who is paid so little that the family remains below the breadline.

The emphasis on child poverty, rather than just poverty generally, is partly aimed at deflating this tendency to blame the poor - the argument being that you can't blame the children for their situation - but it has still failed to energise public support for the cause. Government action has been taken in spite of this apathy, rather than in response to popular pressure. "People find it easier to send money to buy a goat to help villagers in Africa than to help tackle poverty here," Fisher says, highlighting a reluctance to confront the causes of poverty at home, bred partly from an unwillingness to accept that the answer may lie in the need to redistribute wealth.

"We are not suggesting that this is the poverty that you see in Mumbai. Poverty here is not as extreme, but it is still dire," says Martin Narey, chief executive of Barnardo's. "We don't have to choose between helping the developing world and sorting out our own society."

Tim Nichols, of the Child Poverty Action Group, agrees. "Of course children who are affected by famine and war are in the worst situation imaginable, but that doesn't mean we don't have our own problems in our own society that are morally unacceptable," he says.

Louise is conscious that her situation is not one that usually attracts much sympathy. She hates to be cast as "the stereotypical single mum on benefits, sitting on my bum living off other people's taxes". She points out that she was in a serious relationship when she had her children. "I wasn't young and foolish. Their father had a job," she says. Since he abandoned them he has paid no maintenance, and Louise is so disillusioned that she says she never wants another man in her life.

She absolutely agrees with the government philosophy that work is the best route out of poverty, but she does wonder how she is ever going to find a job.

"Of course I'd rather be working than being on benefits. If I were working, I wouldn't be living in a two-bedroom council flat, underneath someone with mental-health problems and a couple of addicts. I'd have carpet that fits and lino on the floor," she says. But she doesn't expect to find work soon. "My CV would say: left school. Worked one month in a nursing home. Got pregnant. That's not going to get me a job. There aren't enough jobs to go around."

In between walking her daughter to school at nine o'clock, taking her son to nursery at one, picking her daughter up at three and collecting her son at five, she is fitting in computing courses and working on her literacy at the local community centre. "I don't want to be Es, Fs, Gs for ever, so I'm trying to improve," she says, referring to her GCSE grades. But is dubious about which jobs would fit in with her childcare commitments, and she knows that work is increasingly elusive. Few of her neighbours are working and she has to think before she can remember which of her schoolfriends managed to get a good job. "Two girls got a job in Savers, a cheap chemists. I don't know anyone else who's working, except a boy I knew, who wasn't even really a friend. I know he's got a job at the bingo hall, cleaning," she says.

If Louise is not given to complaining, the women who run the courses at the local community centre are very angry. They believe that the people on this estate are beyond the reach of most government programmes, because their deprivation is so extreme and they are concerned that things are getting worse.

"We try to help young people get out of poverty in the way that the government advises - primarily through work - but it has been very hard to find these people work. Many of them are not work-ready. We have to teach them to read and write first," one community support officer says, asking not to be named, afraid that her bluntness would offend the people she is helping.

"The biggest problem is breaking the cycle of lack of educational attainment that leads to poverty. If they could read and write then we could get them into work. As it is, there are real problems with their understanding of things and their retention. It's not something we can help with overnight."

In the 60s, some of the children who went to the local schools in Hartcliffe became bankers and accountants, she says. That doesn't happen now. "Good teachers don't want to teach here. But that's not the only issue. Because we've had generations of poverty here, it means your parents won't have the skills to help you fill in a basic job application," she says.

"Your health will suffer because you won't be eating sufficiently nutritious food. People on a low income don't buy the right food. If you've got a pound, you can buy three packets of biscuits or two bananas. Which are you going to buy if you're not eating very much?"

Louise is already worried that her daughter, Abigail, will soon find herself in the same cycle of deprivation that Blair promised to eliminate. "There is a stigma attached to this area. The teachers think that the children from here are all thick and they don't bother with them. I'm worried that my daughter won't do as well as she could. She's a clever little girl but all that's offered is a basic level of learning," she says.

She is right to be concerned. Research suggests that by the age of 22 months, a child living beneath the poverty line begins to fall behind peers from richer families, and by the time they turn six, previously less-able children from wealthier backgrounds will be ahead. Children living in poverty are only a third as likely to get five good GCSEs as their richer classmates, and five times less likely to go to university.

"It's a bit of an unfair innings," she concludes, the nearest she comes to complaining. "We're all entitled to a good education, but the people whose parents don't have money, don't get it. You don't get a good education, so you don't get a job. It's all down to money."

This is a background anxiety that weaves in with more pressing concerns about how much money is left on the gas meter (she checks in the cupboard, and is reassured to see £3.45 flashing in red digital figures). She is already worrying about how she will be able to afford new school uniform for the children in six months' time, given that she is still paying off the loans she took out last September for this year's batch. She worries about whether anyone will take her concerns about her son's development seriously. She worries that the frozen mince she feeds her children is watery and poor quality.

By Thursday evening she's down to £2.05 (£3 went on a replacement birth certificate for her daughter) and she has decided to use the emergency £10 she keeps in a china jar on the windowsill to take the children on a bus across Bristol to spend the weekend with her mother, Nicola.

Nicola, who is also out of work after losing her job as a cook for the Salvation Army, is happy to help. When Louise was a child, she used to feel insulted when the school handed out food packages donated by the Lord Mayor for the city's "underprivileged", but she thinks her daughter has a harder life than she ever did. She believes the government is ill informed about the depths of deprivation that still exist. "When politicians come here, they get shown a very sanitised version of reality - the community centre is given a lick of paint, and a few local residents are carefully selected for them to meet. They don't see how it really is," she says. "They need to come and see how she's living."

Campaigners here insist that despite the huge scale of the challenge, reducing child poverty to match the levels in the better-performing European countries is not an unrealistic goal. They say putting £4bn in the next budget towards extra means-tested benefits for the poorest would go a long way towards helping meet the 2010 deadline of halving the number of poor children. The longer-term goal requires a mixture of investment in schools and training and measures to end social exclusion. "Finland, Sweden and Denmark have child poverty levels of 7%-8%. There's no reason why we can't be at that level," says Nichols of the Child Poverty Action Group. "The target is eminently achievable."

Louise hopes her children will have a better quality of life than she has. "I'll tell my children they can do anything they like. I want them to get jobs. It would be nice if they did something that earned them some money," she says. In the meantime, she is determined to preserve an optimistic outlook. "You can't wake up in the morning and assume it's going to be a good day, but I am a positive person. I think you have to take life as it comes".

'We get by': Louise's weekly shop

Morrisons

Rathbones loaf of bread 0.99

"M" frying chips 0.79

"M" wheat biscuits 1.15

Hot-dog sausages 0.47

Hot-dog sausages 0.47

"M" apples 1.00

Petit filous 1.00

Petit filous 1.00

"M" value orange juice 0.56

"M" peanut butter 0.78

"M" mature cheddar 1.99

"M" fresh milk 2.25

Danish Orchard jam 0.95

"M" granulated sugar 0.93

Total £14.33

Iceland

Pies 1.00

White potatoes 1.00

Dairylea spread 1.00

Ham and pineapple pizza 1.00

6-pack bananas 1.00

Total £5.00

• Names have been changed.