Despite statutory anti-bullying policies and the best efforts of many schools, bullying continues to plague some children’s lives. The human cost - in terms of young people who drop out of school, develop phobias or eating disorders or attempt to kill or hurt themselves - is immeasurable.

The catalogue of harm inflicted this year alone illustrates the problem. Two teenage boys from London’s East End were sent to prison this summer for blackmailing a fellow pupil out of pound;10,000 - his grandmother’s life savings. An 18-year-old boy hanged himself from a tree after being teased and bullied at school. And ChildLine has reported a record number of primary age children calling to talk about playground misery.

There is no single solution to the problem of bullying, but there are a growing number of ideas about how to deal with it. The anti-bullying charity Kidscape, under the energetic direction of child psychologist Michele Elliott, has developed a new strategy in the form of the ZAP programme, which offers training for the victims of bullying. “The children typically come from supportive, loving, intelligent, sensitive families,” she says. “They make good victims because if someone shouts at them or treats them unfairly, it’s outside the realm of their normality.”

Many of the 11,000 parents who call the Kidscape helpline every year are looking for specific help for their children, particularly if the bullying has been going on for some time. “Parents say their children don’t want to go to school, can’t talk to other kids, have developed a victim mentality. They want to know where they can go to get their children to feel better about themselves,” says Michele Elliott.

Which is why ZAP was devised. This half-term, 12 young people aged between 10 and 14 converged on Kidscape’s offices for a half-day course designed to increase their self-esteem and reduce their sense of isolation.

Here in the shabby grandeur of Grosvenor Gardens, near London’s Victoria station, there is nothing to mark out the children as victims. Helping themselves to custard creams, crisps and Coke, they look like any other group of kids - mixed shapes and sizes, some more outgoing than others, some wearing glasses or braces, all in trainers and sports gear.

They begin the day by sharing their experiences of being bullied. “It’s quite easy to talk,” says 14-year-old Richard, humorous, plump and bespectacled. “I don’t know the others, and I won’t see them again in my life.”

He has been picked on by children in his class for a couple of years, he says, and has been hit on the head with a pile of dictionaries, called names and punched. “I try to tell the teachers,” he says, “but my head of year intimidates me, and my form teacher seems to do nothing.” His mother contacted Kidscape last year when she noticed bruises on his arm.

While the children swap stories of being cold-shouldered, assaulted, insulted and intimidated, the parents take themselves off to a nearby coffee shop and compare notes.

Thirteen-year-old Rudi, a slim, dark-haired boy now in his third year of secondary school, came close to a nervous breakdown a few months ago, says his mother. He was one of a dozen children in his year group nicknamed “The Outsiders” because they belonged to neither of the two large gangs at their Catholic foundation school in the home counties. Such was the hold gang members had over Rudi that he was not allowed to get off the bus until they said so, or eat without their permission. He was also, at their direction, stealing from his mother’s purse.

But when Rudi’s parents tackled him over pound;300 which had gone missing, he didn’t tell them the reasons for it.

“His father gave him such a clout,” says his mother, 34-year-old Christina Chandler, “but he put up with it rather than say what was happening, because he was so frightened.” Soon afterwards she took a day off work to talk to Rudi about what was wrong and he “snapped”, and told her the whole story.

“It was amazing how much it had affected him, and how far it went back. He’d even thought about suicide. Looking back on it, he had tried to say something at odd times, but there are four children in the family and we’d been so busy. We said to the head when we saw him, ‘Not only have you let him down, we’ve let him down’.”

Rudi, who is dyslexic, stayed out of school for six weeks, and went to pieces whenever it was suggested he return. He is now at another school. Although the bullies tried to follow him there - they began congregating at the school gates in the afternoons to threaten him - firm action by the headteacher and threats of police involvement put a stop to it.

Rudi is taking part in a session on self-defence run by Michele Elliott. She often suggests to parents that they introduce their children to martial arts, “not to turn them into Rambos, but to give them confidence about how they walk and talk”. Today she demonstrates simple moves to “get out and get away if someone is attacking you”. She shows them how to escape someone grabbing them from behind, and to general giggling they get into pairs to practise kicking an assailant in the knee and stamping on their foot. “If you’re ever in real danger,” Michele Elliott tells them, “break a window.” While cries of “help” or even “rape” are often ignored, the sound of breaking glass always attracts attention.

The children proceed with another adult trainer to discuss body language, act out ways of ignoring and diffusing taunting, and finish with a group discussion of how they relieve frustration at home after a day’s torment at school.

At the end of the session, Kidscape staff give out contact lists so children can keep in touch. This potential extended social contact can be one of the most helpful experiences for these children. Fourteen-year-old Tim Mackeson, the oldest of three boys in his family, did the ZAP course in the summer after persistent bullying at his north London comprehensive. “I got to know a couple more people who’d been through situations like mine,” he says. “I made quite a few friends out of it. No one picks on me now. They can’t be bothered any more.”

Is there such a thing as a natural victim? Haydn Powell is head teacher at Brampton Manor school in Newham, east London, where two pupils began a long-term campaign of extortion against a vulnerable boy in the same year group which ended with a successful prosecution. All three boys had left the school a year before the case came to court and, says the head, “we were unaware of what went on. This boy hadn’t told anybody in the school anything about it. He was one of life’s victims, lacking in confidence, very quiet, someone who holds things within them. We try to give strength to friends in that situation, to help, but he was a loner, which made him even more vulnerable.”

To his credit, Mr Powell admits that his staff are dealing with bullying “all the time”. He says: “I told new parents last week. ‘Yes, we have lots of bullying. And this is what we do about it’.”

But are some children really impossible to protect? Michele Elliott thinks not. “You do have some kids exhibiting chronic victim behaviour. Other children may not want to be friends with that person, but they can be friendly, they can be nice. They don’t have to be overtly unpleasant.”

According to the evidence of parents calling Kidscape, some schools are doing far better than others in dealing with bullying. “We know there are masses of schools out there doing brilliant work,” Michele Elliott says, “but it is interesting that over the years many of the calls come from pupils at the same schools, or sometimes the same local authorities.”

Many of the children doing the ZAP course have experience of several schools and have only been able to emerge as non-victims with the right support. “In some schools there is a bullying culture,” says Michele Elliott. “Bullying within the staff or from the top down. In others, teachers don’t feel supported and they put their head down and teach their subject, because all they want to do is get through the day. Bullying is not character-building, it’s character-destroying.”

One strategy increasingly found in secondary schools is the use of other children to help troubled pupils. At the 2,000-pupil Kingsbury high school in Wembley, 20 sixth-formers have been trained by Relate, the relationship guidance organisation, in how to listen to their peers.

Head girl Asha Katwa, 17, volunteered for the training because: “I went through some girly bitchiness in GCSE year. It’s all about competitiveness. There’s ‘pretty’ groups, there’s ‘intelligent’ groups.”

Ita McNamara, head of Year 9, is PSHE co-ordinator and responsible for setting up the peer listening project. “We had a PSHE programme, but I felt we needed to develop something more for our students,” she says. “Adults only hear half the story. I do think youngsters will communicate more of what they feel to older pupils.”

With a grant from the Mental Health Foundation, students were trained and nine staff went on a short course to learn how to support the sixth-form listeners. This aspect is important, as students may hear about suicidal impulses or abuse. They need to be able to pass on to an adult what they can’t deal with themselves.

The listening service, called Connect, now has a dedicated room in the lower school, shared with the school counsellor. Listeners have given assemblies, made presentations to tutor groups and taken their services out into the playground. Now they are planning assertiveness training sessions and self-esteem workshops.

“It’s quite unbelievable how it’s grown,” says Ita McNamara. “It is a lot of hard work though, and it needs co-ordinating. You need staff and youngsters willing to get involved and total commitment to it.”

Research from Roehampton Institute on the effectiveness of peer support in challenging bullying has found that, over time, these systems can improve the general social climate of the school and that users find them helpful. However, boys who try to get involved as supporters can find themselves undermined by ridicule from fellow pupils, and both boys and male teachers are under-represented in peer support schemes.

Theo Haet, 17, says pupils sometimes have unrealistic expectations. “Some of them come expecting you to solve everything, and when they don’t get that they feel as if they’ve wasted their time. You have to make them understand that this is not some sort of vigilante thing.”

Fellow listener Michelle Yong, 17, explains the principles of Connect. “When somebody comes with a problem, normally you tell them what to do. We’ve learnt to listen, and let them work out what to do for themselves.”

All bullied children’s names have been changed. A Kidscape conference on bullying, suicide and self-harm takes place on November 11 at The Law Society, London. Cost: pound;75 per place including lunch and 260-page book ‘How to Stop Bullying’. Some bursaries available. For details contact Lisa Flowers on 0171 730 3300.