Christmas morning in Korogocho will smell of charcoal and chapattis. By dawn 100,000 cooking fires will be alight in the great Nairobi slum, the most densely populated place in East Africa. And from the mud huts and tin shacks will come the sizzle of chapatti dough as it rises, bubbles and burns a little on a flat iron pan. Kenyan chapattis are greasy, heavy and strangely delicious if you're hungry: monster crêpes. And they are Christmas food here because, like festive food the world over, they are special: something that you don't eat every day.

The ingredients are just flour, salt, oil and water - but the flour is from wheat, and very expensive. A normal meal here is maize flour boiled into ugali porridge. I asked 12-year-old Kelvin Murage what the best food that he could imagine for Christmas was. “Chapattis, of course,” he said. “Chapattis for breakfast, lunch and supper.” He gave a wide grin. No hungry boy ever awaited turkey and trimmings with more excitement.

While their grandmother fries the chapattis, Kelvin's ten-year-old sister Beatrice will unwrap a longed-for pair of red sparkly shoes. They would probably be recognisable to you and me as Dorothy's footwear from The Wizard of Oz, though Beatrice has never seen the film. Kelvin will get a pair of suede safari boots, and six-year-old Griffins a garland of green and pink plastic flowers. He showed them to us in the market. Why those? “I want to decorate the house,” he said, solemnly.

The house could do with it. The roof is partly sacking, partly rusty tin: it sags and lets in brilliant shafts of sun - and, of course, rain. The walls are red mud and in places the sheet metal of oil barrels stamped flat. There is no adornment to the two small rooms, just hangers on a string to keep the family's few clothes out of the dust. An open drain runs across the little yard where the children play. But it's a safe place. Outside there is danger.

We are told not to wander in the little alleys because people will poke knives at us from inside their walls - a way of scaring away intruders. We see stoned children sniffing glue. The policeman whom we have been advised to hire for security (for 1,000 shillings, or about £9, for the day) tells us that this is the most dangerous part of the slum. Normally he would never come here, he says. In the gutter outside, pigs root among raw sewage and plastic bags. The word Korogocho means “worthless place”.

We know what the children will be getting on Christmas morning because we went with them a few weeks ago to windowshop in the busy clothes market. Here you meet the end of the line that begins in the charity shops of Europe - Korogocho, which is home to 315,000 squatters, is where our unwanted clothes become objects of desire again. There are bundles of jeans and T-shirts, baseball caps, shirts and great piles of used shoes. I couldn't help checking out the T-shirts and their slogans, thinking that there might be something amusingly retro to take home. “My other girlfriend's a supermodel,” it said across one crop-top.

Picking through the used shoes, Little Beatrice spied something. The red slippers. “Mzuri!” she breathed, her eyes shining, as she put them on. She twisted her feet so that the spangles caught the light. “Nice!” We asked what she would do with them - if they were ever hers. She thought seriously about it: “I would wear them on Christmas Day to go to church. And I would wear them once to school, so everyone could see them. And then they would stay at home.” She tried a catwalk stride, lifting her feet carefully so that the shoes, a size too big, didn't fall off. She bent and peered at them, brushed away a speck of dust. Little Beatrice was in love. When her back was turned, we bought them for 250 shillings (about £2.20). How could we not?

What would you like for Christmas, I asked Grandmother Beatrice. “I have everything I want,” she laughed. “I have a dress I like, a warm sweater and some smart shoes for church. They are white leather, with laces. But if I had some money I would buy a paraffin lamp so the children could read at night.”

Clothes and food are traditional Christmas gifts in Kenya. A new dress is what every woman hopes for and expects - “there will be trouble in the home if there aren't any new clothes at Christmas,” I was told. We found the little tailoring businesses that line one of the market streets very busy. Ancient foot-pedal sewing machines whirred their way through bright artificial silks. It costs 800 shillings to have a two-piece made, suitable for church on Christmas Day: this year's fashion is big shoulders on the jacket and a fishtail to the skirt: tight to the knees, then flaring out.

On the market stalls were some of the paraphernalia of modern Christmas: a 4ft plastic tree, some strings of fairy lights and grubby tinsel. The tree was 400 shillings - to me. Like so much in the market, all these had been retrieved from the great city dump, Dandora, which rises beside the Nairobi river, just outside the Korogocho limits. We window-shopped a bit more, fascinated by the industry that recovers everything of possible value from what the rest of the city has discarded. There were rows of computer mice, hanging by their tails from a rail. Bent bicycles. Endless broken bits of electronica. Stacks of used paintbrushes. Stacks of used toilet brushes. And a box of vibrators - used, too.

At 10 o'clock on Christmas morning, Beatrice and the children will walk the quarter of a mile through the alleys to church. This is a shaky structure of plywood and tin, as high as a two-storey building, with a big sign proclaiming it the Damascus Assembly of the African Divine Church. On weekdays it is a primary school, privately financed and run. Among its 350 students are the Murage children. Most of the slum is Christian, though there is a small mosque and an Islamic school as well, serving the many Somali refugees.

Christmas service lasts for two hours, Pastor Peter Idaki told me. Isn't that awfully long for children? “Ah, but there's lots of singing,” he said. “And cake.” In the middle of the service a huge iced Christmas cake is cut up and served with orange squash to the 200-strong congregation. It is an annual gift from a local woman whose business thrived after the pastor prayed for its success. “I have to admit,” he said, his eyes twinkling, “some of the congregation attend because of the attraction of the cake.” There are prizes, too, for the best singing teams in the congregation - last year the winners received plastic cups.

What do they sing? He mentioned a few titles in Swahili - I looked blank, so he sang them in his lovely tenor, and there were the familiar tunes: O Come All Ye Faithful, Once in Royal David's City and Hark the Herald Angels Sing, which translates back as “The angels sing a very good song”. “Christ the Lord” in Swahili is “Christo Bwana”.

What happens after church? “People walk around if it's sunny,” said Pastor Idaki. “They go to see their friends, show off their new clothes, talk. The children like to play with balloons in red, white and green - these are the Christmas colours and the Kenyan colours, too. Some young men will play football. They might go down town to Uhuru Park. But mainly we'll eat chapattis and have fun with our friends.” Just chapattis? “With chicken if we are very lucky. But most people will eat them with beans. It's a happy day. Everyone is glad to be on holiday.”

You can understand that. People in Korogocho seem to work harder than any others I've seen. Everywhere you look in the slum there is industry. Someone is cutting up old denim to make into school bags, or carving lorry tyres to make sandals. Goods from the dump for are being repaired. Most houses have a stall with odds and ends for sale out front. The people here are mainly new arrivals from Kenya's hinterland, all looking for work. Some are refugees from the ethnic violence that ravaged the country after disputed elections at the end of last year.

Korogocho is also a trap of filth, violence and hunger. Gunshots ring out periodically during the day: Caroline Irby, our photographer, became caught up in a mob fleeing one gun battle.

“Murder, robbery, it happens all the time,” 13-year-old Margaret Wamboi told me. “It's very frightening but you can't help people if they are attacked. That is too dangerous.” She and her 16-year-old sister look after six younger siblings and cousins, all of them orphaned by Aids. When I asked her what she wanted for Christmas, she told me first, food, then storybooks. And then: “Sponsorship so I can go to secondary school.”

Grandmother Beatrice has four grandchildren to support (there is another brother, Christopher) and a sick daughter. It is very important that the children are well fed: Little Beatrice and Griffins are both HIV-positive. Their strength must be kept up to avoid secondary infections, and the strong anti-retroviral medicine that they take (which the Government provides free) must be swallowed on a full stomach.

The Murages and the Wambois are beneficiaries of an innovative and clever aid plan for which you - the British taxpayer - can take some credit. With help from the Kenyan Government, this provides an extra 1,500 shillings (about £12) a month to households with children who are orphaned or deemed vulnerable. Pastor Idaki is on the volunteer committee that identifies the needy families and helps to monitor how the money is spent. The beauty of the plan, as Ada Mwangola, of Britain's Department for International Development (DfID) in Nairobi, explains, is that it takes little administration.

“It's very cost-effective. Transferring cash can be much better than transferring food,” she says. “As long as there is food to buy in the market, this works well and it is preferred by the recipients. It allows them to make decisions about what they need to spend the money on: it may be food, a school bag, some books or shoes, or a goat that they can milk - which will have a baby goat they can sell.”

The only conditions attached to the cash are that children must go to school, have identity papers and go to health clinics. As the scheme rolls out across Kenya the DfID will spend £40 million over ten years, with Kenyan taxpayers matching the amount.

There is no doubt that the “city money” has made a difference to Beatrice Murage's life. She used to earn her living scavenging on the Dandora rubbish mountain, sifting for bits of plastic or metal to sell to scrap dealers. The work was dangerous and unhealthy - everyone in Korogocho, according to the United Nations, has too much lead in their blood because of the slum's proximity to Dandora. Beatrice used to go there every day. The “city money” pays her rent and leaves enough to buy adequate maize flour to feed the whole family.

“Without the money,” says another volunteer, Jennifer Otin, a schoolteacher, “these families would break up and things would be much, much worse for the children.”

Grandmother Beatrice took us to the dump, a great stinking heap that stretches to the horizon. Street children play among the bulldozers and lorries, and all over the pile are human beings scrabbling for anything sellable. Standing on the giant heap of refuse, she waved us a cheery goodbye.

I'll be thinking of Grandmother Beatrice and Little Beatrice on Christmas Day: down at the bottom of the world's heap but still able to find joy in a day off, a pair of shoes and something special to eat.

More information on the DfID-backed programme for orphans and vulnerable children in Kenya at www.dfid.gov.uk

Christmas wishes

Children in the Korogocho slum, Nairobi

Mayasimu, 4: a mobile phone

Josiah, 11: a toy soldier or a portable radio

Michael, 10: a toy car

Sitikate, 6: chicken, chapatti and orange juice

Celestine, 4: shiny black shoes

Marya and Miriam, twins, 3: meat and chapattis

Catherine, 4: a smart dress

Helen, 3: cake

Margaret, 13: food for my family and some story books; sponsorship for secondary school

Beatrice, 10: red shoes

Kelvin, 13: some good boots

Griffins, 6: some plastic flowers to decorate the house

Alvin, 13: some new corrugated iron sheets to cover the holes in our roof so the rain stops coming in.

Cliff, 9: some new clothes - “really new ones, not second-hand”.

Ronaldo, 15: “The gift I really want is sponsorship so I can go to secondary school”

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