She emerges from a narrow alleyway, unsmiling, her waste wrapped up in a black plastic bag which she throws into a dirty, disease-infested ditch, one of many running through the Mathare slums on the outskirts of Nairobi. Three years old, orphaned, her parents died of Aids and she lives with her brothers and sisters in a rusted tin shanty, held up with timber and mud and measuring no more than 100sq ft. Her oldest sibling is 12, the head of the household, responsible for paying the rent of £6 per month. They sleep on pieces of cardboard on a dirt floor and have no electricity, no running water and no toilet, so they use plastic bags and a ditch, really an open sewer. “Flying toilets” they call them.

“How many people are here?” asks Martina Navratilova as we walk through an area of humanity which is, in effect, “a disaster zone”. The nine-time Wimbledon singles champion is an ambassador for the Laureus Sport for Good Foundation, which lends support to Mathare Youth Sports Association (MYSA), a remarkable group of local young people out of Mathare’s population of more than 600,000. “That’s 200,000 people per square mile,” Navratilova responds incredulously when Peter Karanja, MYSA’s 31-year-old director, supplies her with the information. “That’s ridiculous.”

This is one way to characterise the squalid, claustrophobic conditions here, a monument to illness and impoverishment lying, barely believably, across the road from an expanding neighbourhood of luxury homes. When the lights of these houses shine like beacons, Kenya’s great divide could be no more apparent. It is estimated that one in every three adults in Mathare is HIV-positive and, once infected with the virus, the average life expectancy is less than five years. There are 70,000 children living in the slums and they are susceptible to infection, malnutrition, malaria, typhoid, cholera, tetanus, dysentery and polio.

Child prostitution, drug abuse and crime present further endangerment, along with recent barbaric acts carried out by the Mungiki, a cult-like group described by some locals as “devil worshippers” who “drink blood”. They are also racketeers, levying bootleggers on their homemade brew, changaa, and terrorising people at night, even beheading defectors. When two police officers were gunned down by the Mungiki in June, police entered Mathare with machine guns and in the ensuing chaos 30 people were killed, hundreds arrested and thousands forced to flee.

Meanwhile, people get by, occasionally finding a job that will pay 50p or so a day, enough to buy paraffin for the lamps or to secure the next meal. “It’s amazing that these people survive,” says Navratilova, passing a cart filled with fruit and vegetables and a secondhand clothes shop that is closed, the unrelenting smell of refuse hanging in the air. “It makes you think we haven’t evolved much as a race that people live in these conditions and nothing’s changing. Shame on the Kenyan government, who don’t have to put up with conditions like these themselves, yet they allow this horrific situation to continue. How can they when they could build high-rises? I mean, look at the children. They have no place to go and they’re the ones you want to help the most, and make it good for them or at least better. You’d love to be able to wave a magic wand so that these sewers are gone and they have an underground water system, toilets, running water, a separate kitchen and bedroom in their homes and all the garbage is on a compost heap where it can do some good, instead of littering the area and creating serious problems when it rains.

“All of this makes you want to yank all these people out of here, the kids especially. They’re eager and capable, very bright. They want to do stuff, but how do you go from here to being successful in life? It’s very difficult. You have to be so brilliant that it’s not fair. I was lucky that I was born in the Czech Republic. It’s bad that it had a communist system but, considering all of the places in the world in which I could have been born, I was lucky. Opportunities were there, like the four tennis courts in my town. Here people struggle to get clean water, so tennis isn’t going to help. Tennis helps people when they get to a more normal stage of living. This isn’t normal living. This is unacceptable. Unfortunately, it is normal for these people. They’re beautiful and they’re clean and they have a smile on their face, yet this is a disgusting environment. The adults have managed to build up an immune system which is stronger and they can deal with the germs. They can also walk out of here and try to make a living somewhere else but the children, they have no choice and I’m thinking, ‘Can I adopt 10 of them?’ I just want to do something, a typical reaction.”

Bob Munro, a Canadian expert in environment and water resource management and sustainable development, felt a similar compulsion to do something when he arrived in Nairobi 30 years ago to work on United Nations relief programmes. When he came across some children kicking a football made out of plastic bags one day in Mathare he realised sport could be a powerful vehicle. In 1987, with the help of members of a youth group formed by St Teresa’s Catholic Church, he established MYSA as a small, self-help youth project with modest aims to organise sports. For Munro, this represented a kind of repayment to the volunteers who organised youth sports leagues when he was growing up in St Catharines, Ontario. For the youth of Mathare it was a new beginning, empowering boys such as Karanja, the present director, and Simon Muindi, MYSA’s communications officer, to aspire to much more than the winning of a football game, even if this was, and continues to be, their inspiration.

From a starting point of 25 boys’ football teams, MYSA has grown into the largest youth sports organisation in Africa and a model for similar projects in other countries. Today there are 18,000 members, 1,128 boys’ teams and 269 girls’ teams. Mathare United, a professional team made up of the best players from MYSA’s leagues, is one of the top club sides in the country, competing for top spot in the Premier League and grooming players for Kenya’s national teams. On the eve of last year’s World Cup final, with eight MYSA players in the squad, Kenya beat South Africa 4-3 in a penalty shootout to win the inaugural Street Football World Cup in Berlin. The local and international success of their youth has increased self-esteem throughout the entire community.

MYSA, which has been funded by donors from the outset, emphasises the link between sport and service in the community. Points are awarded to teams not only for winning games but for completing environmental and arts projects. Many people have been trained as HIV and Aids counsellors, and even the players of Mathare United commit to at least 60 hours of community work a month. “What I like about MYSA’s work here is the integration of all the programmes,” says Navratilova, who retired from tennis last year to dedicate more of her time to similar projects. “We always compartmentalise things but everything is connected, in reality. That’s what they get here, that sport is connected to the society around them, it’s connected to art and to community involvement. If you’re not in good physical shape, you can’t think well and they understand this here, and that’s what’s so encouraging and why it’s working and is able to sustain itself. The kids who have come through the programme are now the leaders of the programme, which gives you hope because they’re motivated to get things done. Charity is bullshit. You need to give people the means to sustain themselves, to empower themselves to take care of themselves. That goes much further.

“We don’t know what might have happened to these kids if they had not had the chance to play football and become leaders in their community. It’s like a seed. When you seed something and it flowers then that first flower creates 100 flowers. It’s the same here. You help one kid and that kid helps another kid, and those kids help 100 more kids. Where would all these people be without this programme? We don’t know. We just know that they’re better off than they would have been. I remember when I first came here in 1997 I befriended one of the boys who would guard the car when I went to the shopping centre. He told me that he wanted to be a carpenter but didn’t have the tools and I dismissed him, thinking he only wanted a handout, but this boy was different. So I bought him what he needed and within months he e-mailed me to tell me he was in business. The opportunity to reach their potential and to achieve their goals and their dreams, that’s all these people want and that’s what MYSA and Laureus are trying to give them.”

From nothing, Mathare’s youth are building something, transforming lives and making a once invisible problem visible. People in power still turn a blind eye, but by empowering themselves through sport they see hope in their future.