The remote island of Ukerewe, several hours across Lake Victoria and two days overland from the capital of Tanzania, is the one remaining shelter, a place where albinos can live in relative safety.

"Life is better here on the island," says Alphonce Kajanja. Standing in Ukerewe's main market he is just like any other fishmonger, only his hat shades a white face with swollen liquid eyes and cracked lips. He says there have been no albino murders on the island. "People here don't believe in this satanic campaign."

Elsewhere, the killing continues. In the past week, two more Tanzanian albinos were murdered. Elizabeth Hussein was hacked to pieces by men with machetes in Shinyanga province last Tuesday. She was just 13. Then Ezekiel John, 47, was shot and had his arms and legs cut off near the city of Kigoma on Thursday. Their deaths bring the toll to 35 murders in just more than a year.

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There is similar violence throughout east and central Africa. And even in west and southern Africa, albinos face persecution and discrimination. The campaign is being orchestrated by witch doctors who claim they can make people rich using limbs and blood from their white-skinned neighbours. In some areas, albino children go to school with bodyguards, others hide at home, and distraught relatives pile rocks on their dead loved ones to deter grave-robbers.

I had been brought to Ukerewe by the Tanzanian Albino Society, an organisation set up to fight discrimination which is entirely funded by the UK-based charity Action on Disability and Development, one of the three charities being supported by this year's Independent Christmas Appeal. Ukerewe is believed to have the highest concentration of albinos in the world. No one here is sure why there are so many zeru, the Swahili word for "ghosts". Some believe an unknown mineral in the fish the islanders live on makes mothers have albino babies. Others say intermarriage has bred an increased minority compelled to stick together.

Ukerewe's elders tell a different story of a nearby islet of Kilita where unwanted albino children would be dumped by families that could not bear the stigma. According to this tale, fishermen would sometimes take pity on the abandoned ones and take them in or give them to families they call "samaritans" on Ukerewe.

Whatever the cause, among the tin shacks, fishing dhows and tropical fruit trees of Lake Victoria's largest island there are an extraordinary number of people with the distinctive white skin, gingery blond hair and pale eyes.

Albinism is an inherited disorder. It derives from a congenital lack of the melanin pigment which protects the skin, eyes and hair from the sun's ultraviolet rays. Some have very poor vision, though not all have red eyes as myth often suggests; most have blue, others have hazel or brown eyes. But all forms of albinism are associated with vision problems and those who have the condition are "legally" blind.

What all albinos have in common is that they are rare. In most parts of the world, only one person in 20,000 has some form of albinism. In Denmark, the prevalence is one in 60,000, but in Africa it is thought to be about one in 5,000. In sub-Saharan Africa they are immediately visible; too white to be black.

In Tanzania, an east African giant of a country that stretches beneath the equator from the Indian Ocean to the great lakes of Victoria and Tanganyika, people are five times more likely to have some form of albinism. Estimates of the numbers of albinos in the country differ, some are as high as 200,000, all of them complicated by the stigma attached to their condition which in many cases makes their family hide them from the outside world. But the prevalence has led many researchers to consider whether the original genetic variant may be traceable to this region of East Africa, or even to Ukerewe itself.

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Counting his tilapia fish on the slab, Alphonce Kajanja has a simpler explanation. "When God saw how they treated us, the names they called us and how they killed their own children, he sent them more albino children. We are a punishment from God."

Until now, the fishmonger's main enemies have been prejudice and skin cancer. At 48, he has so far fended off the sun which burns here with an unforgiving intensity ot his defenceless skin. Thanks to his lifelong hobby of weight-lifting, he has been better prepared than most to confront the other enemy. A son of non-albino parents who accepted his condition, he grew up among the tough streetchildren of Ukerewe's main town, learning to fight for everything. He used that ability to get his pitch in the fish market and that status to get a non-albino wife, an extremely unusual distinction.

He has had five children, none of them albino, and has won the grudging acceptance of his peers. Few have been so lucky. Less than a handful of albinos on Ukerewe have an actual job.

In an already impoverished community, access to the goodwill and charity of the extended family or clan is vital to most peoples' survival. For albinos, a lifetime of social exclusion and abject poverty is all that awaits.

Many albino children, uneducated about their condition, are left to a life of harsh labour in the sun: the result is catastrophic skin damage, agonising side-effects and an early death. Skin cancer means a life expectancy of just 30. None of Alphonce's four albino brothers and sisters have survived.

Beyond the shores of Ukerewe, an even worse fate awaits. The one-time zeru are hearing a different nickname called to them now, "money": they are seen as walking bank notes.

Jospehat Torner is attempting to document the horrific killing spree that has left albinos feeling "terrified and hunted". An albino himself, his outfit is designed for maximum protection from the sun. A baseball cap is pulled down tight to shade his face, and a suit and tie defy the soaring temperature. Despite these precautions, he looks much older than his 34 years.

Mr Torner is a leading campaigner with the Tanzanian Albino Society, an organisation set up to fight discrimination that has found itself fighting for life itself. He says last week's murder of the 13-year-old girl was typical. She had been tempted to leave the safety of her home to see a film about Jesus being shown on a projector near to her village. All the local children went.

On the way back is when those he calls the "greedy people" got her. "They chopped off her legs and her arms," he adds, gesturing with a look of pain as if he was losing his own limbs. The question, he says, is, "Who is the consumer of these body parts? When you go to the traditional healers they say it's the fishermen; when you go to the fishermen they say it's the miners. And they blame the traditional healers."

In fact, the evidence already points in one direction alone, the healers or witch doctors who have started to market albino bones, skin, hair and blood as ingredients in potions that will make people rich. One man was caught trying to enter DRC with the head of an albino child in his luggage. He said he was taking it to a businessman in Congo who was going to pay for the head according to its weight. The severed limbs of Elizabeth Hussein were found on the premises of a local witch doctor. But he was tipped off and escaped police.

Like many members of TAS, Mr Torner has been trying to make himself more visible at just the time where it is most dangerous to do so. Everywhere he goes, he must register with the local police and district commissioner to let them know he is there. His mobile phone, which he must hold inches from his face to see who is calling, so poor is his eye-sight, has been ringing with death threats. "They say to me, 'Where are you? We want to kill you'. And I say, 'fine, let's meet'."

TAS believes its mission to reach out to the multitude of albinos in Tanzania – and educate them, bring them into the open and teach them their rights – is the only way to fight back in what has become a battle for survival. The non-profit group does not have the resources to face the mounting crisis and has been utterly reliant on the British charity ADD (Action on Disability and Development). "Support for TAS is vital if albinos are to secure the of basic human rights of safety, security and freedom," said ADD's acting chief executive, Jabulani Ncube.

Last month, when the death toll stood at 30, TAS drew thousands of people to a protest march to highlight the killings. It organised another protest on Saturday and plans weekly demonstrations through December. The Tanzanian government – appalled to see the country's cherished reputation as a haven of stability and development collapsing – has been scrambling, after an acutely slow start, to look busy. The President, Jakaya Kikwete, was guest of honour at the 19 October demonstration and has recently sponsored the country's first albino MP. Practising witch doctors have been arrested by the score and death sentences threatened to those found guilty; so far, no one has been successfully prosecuted and the killings continue. The fear has reached Ukerewe. In Masahonga, at the end of a 100km dirt road that connects the nearest paved road with the ferry to Ukerewe, a crowd had gathered last week. The district commissioner used a megaphone to hammer home the message that albino murders must stop. In angry Swahili, she denounces the witch doctors as "liars". But the deadly cocktail of traditional beliefs and modern avarice will not be easily neutralised.

Mr Torner has an even darker view. He believes the murders may have been going on unnoticed for many years. Countless numbers of albino babies die in childbirth. "What's to stop a nurse killing an albino baby and saying that it died of natural causes." Nobody knows how many disappeared before people started keeping count. The lives of many albinos have been lived in total seclusion. Inside some homes, albino graves have been dug and marked. People have grown up, he says, being told albinos are ghosts. "We don't die," he says. "We just disappear."

Appeal: Our charities

The three charities being supported by this year's Independent Christmas Appeal are:

VSO (Voluntary SERVICE OVERSEAS)

Sends professional volunteers to live and work in communities in 42 countries. They share their skills with local colleagues to find long-term solutions to poverty. www.vso.org.uk

ADD (Action on disability and development)

Works in 11 countries in Africa and Asia to help disabled people claim food and water, health care, education and other basic rights. Also promotes equality and respect. www.add.org.uk

one world action

Enables poor people in Africa, Asia and Latin America to speak out, helping communities to build democracies and respect human rights, and empowering citizens to challenge bad government. www.oneworldaction.org