It is the simple things that have helped Nikki Leech the most: the reminders to read to her son, the suggestion to make him eat at the dinner table, the persuasion that “no” must always mean “no”.

Nikki, 22, reads to Spencer, 4, every night. If they miss a session, she will make it up by reading two stories the next evening.

Last Friday the two were on the number 10 bus as it wound its way through south Oxford, passing time on their hour-long school commute by reading fairy tales aloud. Nikki laughs as she recalls the trip: “You wouldn't believe it. There I was, on the bus reading Three Little Pigs and acting it out with Spencer. People thought I was a lunatic.”

Until recently, Nikki had not thought it necessary to read to her son. She let him “kick off and get on with it” when he threw a tantrum, and she was puzzled at his refusal to eat his dinner.

She was a struggling single mother who left her boyfriend after violent rows. Spencer was only 12 months old.

The two moved to Oxford and at first received help from Nikki's father, but the relationship broke down when he revealed, during an argument, that he was not her biological father.

Nikki brings up her son on the mantra: “I can't buy it today baby, Mummy's got no pennies”.

She becomes tearful as she tells her story to The Times, for she has been through a particularly tough week - a man that she claims assaulted her last year has been exonerated of any crime. At a time of a national outcry over the horrific death of Baby P, a sense of hopelessness pervades the people across Britain with experiences that are similar to Nikki's. Her case provides a glimmer of hope, however. Her predicament was turned around by a remarkable scheme that she describes simply as her “lifeline”.

In an informal setting in an Oxford shopping centre, the Room to Play scheme offers struggling parents a welcoming environment. There is no need for appointments or any of the bureacracy that deters some parents from approaching social services. Parents are offered support and advice from counsellors to improve their parenting skills, while their children use the play areas.

The programme, funded by the Sutton Trust, focuses on low-cost but effective learning techniques within the home, helping parents with poor sources of income, and often difficulties in communication, to enhance their upbringing of their children.

When The Times visits, several mothers are being shown how to encourage their children to read. A big batch of porridge, which the children are allowed to play with, has been whipped up next to a copy of Goldilocks and the Three Bears. Another group is learning hand-to-eye co-ordination by threading pasta shells together.

With anonymity assured, the organisation has successfully reached those parents, such as Nikki, who are fearful of social services and the stigma attached to reaching out for help.

A draft evaluation on the project, carried about by the University of Oxford, is likely to lead to similar models being set up across the country.

Until recently, Monica's four-year-old boy was hyperactive and misbehaving. While it did not occur to her that his daily intake of sweets and soft drinks was to blame, staff at the centre gently advised her to wean him off. It worked. Monica, 38, told The Times: “He's behaving so much better. It's such a relief.”

In Nikki's case, simple advice made a significant impact. “When Spencer wasn't eating his food, they told me to make him have his dinner at the table. I never thought of that, but it really worked,” she said.

Nikki matter-of-factly counts on her fingers as she explains her household budget: “Every Monday I get £100 from tax credits and income support. That's £40 for food, £15 for gas and electricity, £10 for my bus pass and that leaves £35. I save that and buy Spencer a treat, something to wear. I can't remember the last time I treated myself, I feel too guilty.”

In the evening the pair eat cheaply, with dinners such as spaghetti on toast, pasta, sandwiches, and always a roast on Sunday. Spencer eats bread and butter sandwiches for lunch. “It sounds bad, like I can't afford anything better. It's not that, it's because that's what he likes,” she says.

Until last year Nikki worked as an assistant manager at a factory, but she resigned because she was better off on benefits. “I've just got a two-bedroom flat and if I was working I wouldn't earn enough to pay the rent. I had Spencer in daycare from 7am to 9pm and it was too much, he was getting unsettled.”

She doesn't want the same fate for her son: “I want Spencer to be an air steward. I always wanted to be one and I never got there.”

Nikki abhors social workers, an attitude she developed after a friend's children were taken away. “I don't need them. Whatever you do with your child, it's not good enough for them. I'm strict, I'm a good mum - he goes to bed at 6pm. But they would come in and mess up the routine. I'm the sort of person who would lose my rag with them. I love this programme because they just listen and help, they don't criticise.”

For Sally Smith, manager of the charity programme, the lack of criticism is its key. “We are very flexible, parents can just drop in. The reason that people keep coming back is that they feel valued and accepted, without being criticised. They have shifted in their behaviour but we do it through encouragement.”

Monica, who also has an elder son aged 7, says that the scheme has kept her sane. She was beaten up by her husband for years but left him only when he stabbed her in the stomach. The near-fatal attack left her hospitalised for two months.

Three years later she still suffers panic attacks and depression, which prevent her from working. Ostracised from her parents, she rarely leaves her neighbourhood because it leaves her feeling “disoriented”.

Her boys play inside rather than outdoors; she is more comfortable that way. “This programme has really saved my life,” she said. “I come in every day, even without the boys when they're in school. There are people I can talk to and they are just a constant support.”

Ms Smith said that the scheme often worked as a link to other forms of support, such as social workers, which the women might otherwise have been reluctant to seek.

It is clear that these women are in need of it. More than an hour into our conversation, Monica tells how she was raped when she was 13. She mentions this as casually as she previously said that she does not drink or smoke.

“I feel that I'm coping better with things now, though it is tough at night when I'm by myself and have put the kids to bed. I think about all the things I've had to go through.”

As for Nikki, she is suffering depression and experiencing flashbacks of the alleged assault. But she shrugs and says: “Life can be hard sometimes but I get on, we're doing all right. I don't like to show when I'm upset in front of Spencer. He's my world.”

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