I ask Alastair what was the best thing about being educated in this way. "I could study the word of God every day rather than defending it every day," he states. What did he feel he missed by not being in school? "Temptation," he says, and stops. Alastair is now a tall, formally dressed young man with a direct gaze and a firm handshake, who works for Christian Education Europe. The organisation aims to encourage more families to do as Alastair's parents did and withdraw children from state schools to bring them up as passionate Christians. "Reaching the world for Christ, one child at a time" is its motto.

Although few people outside evangelical churches have even heard of it, more than 500 families in Britain are currently educating their children at home with the curriculum that Alastair's family used. Accelerated Christian Education was developed in the 1970s by American fundamentalists, but its popularity is now growing in the UK, and not only among home-schooling families - more than 50 schools in Britain are using it. The main teaching tools are booklets relating to each subject - the children read a section and then fill in a questionnaire. When I visit the office for Christian Education Europe, in Swindon, I meet one of the directors, Arthur Roderick, who tells me with great gusto that they are getting more and more inquiries every year. "More people understand why we do this now. Black is getting blacker and white is getting whiter," he says, with the rolling rhetoric that betrays his long experience as a preacher.

Roderick points to two big maps on his office wall, one dotted with red stars to show the location of ACE schools and one studded with blue pins to show ACE home-schooling families. They are like the maps of a military manoeuvre and the stars and pins are everywhere. "They go from the wilds of Scotland to the middle of London," as Roderick puts it. But he isn't yet satisfied, feeling that too many people are choosing this kind of education just because they dislike the state system. "The flood will come," he says, "when God touches more people to do it for positive reasons."

Much concern has been expressed about independent faith schools in Britain lately, but the anxiety is always concentrated on independent Muslim schools and what children are learning there. Independent Christian schools, on the other hand, are pretty much ignored. The chief inspector of schools, David Bell, for example, recently criticised independent Muslim schools for failing to teach tolerance of other cultures. But after he had made that speech, his office released information that showed evangelical Christian schools are actually even less successful at that task.

Legislation lays down that independent schools can go their own way in many things - they do not have to abide by the national curriculum - but they must "assist pupils to acquire an appreciation of and respect for their own and other cultures, in a way that promotes tolerance and harmony", and of the 40 evangelical Christian schools that were not yet fully registered by Ofsted, 18 had failed on that count.

The evangelical schools that I visit have, in fact, been deemed to succeed in that requirement, even though they do not see it as their brief to talk about other faiths at all. Where other faiths, or even branches of the same faith, are discussed in the ACE booklets, the tone is telling. One social studies booklet on Martin Luther and the Reformation, for instance, is critical of the Catholic church in the 16th century and also, by implication, today, using such words as "idolatry" and "superstitious nonsense" to characterise supposedly Catholic teachings, and inviting children to underline the "correct" Protestant beliefs. At the Maranatha Christian School near Swindon, 60 children are taught with ACE, which emphasises at every turn that evangelical Christianity is the only route to the truth. In this way it differs fundamentally from the education provided at state faith schools, which put religious education alongside the national curriculum - and can accept children from other faiths and employ teachers from other faiths. At Maranatha, all the families and teachers are literally singing from the same hymn sheet.

The school building is an old farmhouse near Swindon, in a picture-postcard village on the hills. If you wandered into any of the classrooms here during an ordinary weekday, the first thing to strike you would simply be the absolute quietness that reigns under the big posters stating: "God loves the sparrow," or "God made everything in heaven and earth." The children in these classrooms, who are aged all the way up to 18, are sitting at individual desks facing the wall, with high dividers between them so that each has to work alone. This is a characteristic of ACE - discussion with fellow students or a teacher is not encouraged and the pupil studies, in silence, the booklets which begin with Bible verses and thread homilies on good Christian morals through every subject.

Leah, a 13-year-old girl with a ready smile and her hair in pretty clips, moved from a state school to this establishment three years ago. "I had mixed feelings but now I like it a lot," she says. "Sometimes I miss my old friends but I don't think I'd like it at their school - the peer pressure and everything." I pick up from her desk a booklet bearing the word "science" on its cover and open it at random. "I'm certain that you will be very interested in learning about God's creation of Earth for human existence. In his loving kindness our Heavenly Father has provided for all your needs from His earthly creation," reads the first paragraph I see.

Some British state schools have been criticised for putting the creation and evolution as equivalent viewpoints in religious education lessons, but for children at ACE schools the literal interpretation of Genesis permeates everything they are taught. And for the parents who choose schools like this, such literal use of the Bible is the draw. Tom Price has five children at the school, and loves that they are being taught that the six-day creation story is a fact. "Evolution removes God from the world. But I see God's hand in everything. I see purpose and design," he enthuses. Price is a lay preacher in a Pentecostal church, Assemblies of God. "I don't want to have to undo and unpick what they are taught at school."

In addition to frequent incursions of the Bible, ACE also delivers a pretty solid, old-fashioned grounding in other areas. It begins with reading based on the newly fashionable synthetic phonics, and moves on to other core school subjects - maths, history, geography, physics, languages and so on. What stands out is the traditional delivery of the information with none of the role-play and speculation of current mainstream curricula. This is all about getting your head around the "facts" then retelling those "facts" in multiple choice and fill-in-the-blanks tests. Although that means children learn the basics in a way that many state-educated pupils may not, it also means they do not learn to question anything they are taught. Harry Brighouse, professor of philosophy and education policy studies at the University of Wisconsin, Madison, has watched the expansion of ACE in America with distaste. "It is a crude curriculum. It doesn't encourage questioning or individual thought - it is very much based on rote learning."

What is undeniably attractive about this curriculum - even for the sceptical observer - is the way that it moves at the same pace as the child. With ACE, children are assessed on entry and progress at their own speed, working through booklets and doing the tests at the end of each one before they can move on to the next. They work mainly alone, but if they get stuck they put a little flag up in their cubicle and a supervisor will help out. This flexible pace with its built-in checks can clearly work for children who have fallen through gaps in the state system.

One of the parents I meet at Maranatha, Sharon McGowan, has four children at the school. It was the experience of her nine-year-old son that made her turn to Maranatha. During his first year at state school he had a new teacher who had no idea how to teach; during the second year his teacher was off sick and he had a succession of supply tutors. He began to fail. "He really struggled," Sharon says. "He was a proud little boy and when he had to start special classes it had a real effect on his self-esteem. I was worried that he would compensate with difficult behaviour, and I could see that starting to happen." Within one year of starting at Maranatha he had caught up. "He's blossomed." Although Sharon's husband's work is now likely to take them away from Swindon, Sharon is so keen on ACE that she intends to educate all her children at home with it.

Another parent, Des Starritt, tells me that one reason he wanted to withdraw his children from state school is that they were given books about witchcraft there. At first I don't understand, but then I click - he means books by JK Rowling or Philip Pullman. "We would not put Harry Potter in the school library," says Paul Medlock, the Maranatha headmaster. "It is a book without proper values," says Ben Pike. "It treats witchcraft lightly." Pike is one of the trustees of the school, a 32-year-old who works for an IT training company and has three sons at the school. He emphasises that the parents support the school's message. "We come from a range of backgrounds here," he says, "but we have all put our trust in Christ to be our Lord and saviour." The range of backgrounds is not actually that great at Maranatha; almost all the families are white, tending to the less affluent end of the middle class. In London, ACE schools tend to be established by independent churches with Afro-Caribbean congregations.

One such school, the East London Christian Choir School, in Hackney, was set up just a year ago and has a very different setting from the bucolic beauty of Maranatha. An apparently derelict old council building has been carefully done up to provide a small church, offices, cybercafe, and three classrooms, inside which 30 children are working in the distinctive ACE style. "Good morning, Pastor George. Good morning, Miss," they chorus, turning as I come through the door with their headmaster.

This school, church and community centre are the creation of two pastors, Maxine and George Hargreaves, who have a vision for this deprived community. George Hargreaves is a charismatic, articulate man in his late 40s, who recently stood for election for the fundamentalist Christian political party, Operation Christian Vote. He recognises that one of the main reasons children are finding their way to this school is that the state system is failing them. "The fact that even Diane Abbott, our MP, had to take her son out of the state schools shows you what it is like for black children in Hackney," he says.

ACE schools are much cheaper than other independent schools: the reliance on pen-and-paper learning cuts out the need for big investment in resources - they tend not to have science labs, for instance - and the staff (who are often not qualified teachers) are propelled by belief in God to work for very little. By keeping their fees low - this school charges less than £4,000 a year - they provide an alternative to the state system for people who might otherwise have no alternative. Undoubtedly it works for some. One 14-year-old boy here had behavioural problems that had led to his exclusion from a previous school. "But when we actually got the report from that school," says Maxine, "which followed him quite late, we couldn't believe it. He had only been with us for a few months, but it was as though they were describing a different human being. I believe he could go to university." Later I meet the boy she is talking about, working through a booklet giving him comprehension and handwriting practice. "I like working like this," he says of the solitary space around him. "It helps me to concentrate. It was hard to work at my old school."

A couple of the parents are in the classrooms on the morning I visit, and they talk about the way the children are kept free of the peer pressure and low expectations that can have such a negative effect on black children in state schools. Connie Solwah, a former lawyer who works in beauty consultancy, tells me that she moved her nine-year-old daughter out of a state faith school because she felt her potential was not being recognised. "I think it was partly about racism. It isn't easy for me to meet the fees here but it's worth it for what will come out eventually. I want her to develop herself and get the chance to spread out her potential and character."

I can see that here the staff strive to give children a sense of pride. But their learning is shaped by the narrowest interpretation of the Bible with all the preconceptions of this religious bias, including a very particular approach to sex education. Maxine responds first when I ask the Hargreaves about the subject. "We talk to the older girls about virginity," she says. George takes up the theme. "We tell them that the blood shed when virginity is broken on the marriage bed is part of the blood covenant made between you and your husband under God, and if the blood is shed elsewhere it will weaken the covenant." A few moments later, George reaches into his pocket for a tiny pink plastic doll foetus, and drops it into my hand: "180,000 babies like that are killed every year in Britain. That is what happens when you take sex out of God's order."

For parents who mistrust mainstream education, the ACE system provides the means to avoid it completely. The curriculum is easy for parents to use at home because all the information is contained in the booklets, which also provide self-tests and which progress neatly from level to level. And by withdrawing children from school altogether, of course, parents can exercise even more control over what their children think and read and say. I watch Arthur Roderick play to that desire for control when he speaks at a seminar for ACE home-schooling families. "The deepest temptation is up here," he says fiercely, pointing to his forehead. "Philosophical pollution is all around them." Beverley England, who is in the small audience of parents, has already made the choice to save her family from such pollution. She has educated her six children, aged from 20 to two, at home with ACE. Beverley, who found Jesus as a teenager, never wanted her children to leave her home in order to enter the secular system. "I didn't worry that they might be isolated," she tells me. "I knew that if God wanted us to do this he would provide, and he has brought friends to us."

Sean, Beverley's second oldest child, is wearing a baseball cap and jeans, playing jazz piano in another schoolroom while keeping half an eye on some of the younger children. His parents made sure that music and sport went alongside the core ACE curriculum - and he is very positive about his education. "It helped me to motivate myself - I'm a really competitive person and learning to set goals for yourself was really good for me," he says easily.

Sean has a ready smile and an easy articulacy; there is a confidence about him that I also pick up from other older children in this system. Although there is clearly a danger that children educated with ACE, especially at home, could end up unsocialised, it seems to me after meeting a few of them that they are no less socialised than the average product of a mainstream education system that tips a whole lot of 13-year-olds into a classroom together and expects them to get on. Sean, for instance, found friends in his neighbourhood through church and sport and music - the way that adults make friends, through shared interests.

Although ACE-educated children do not take GCSE or A-levels, their own qualification, the International Certificate of Christian Education, is now recognised by more and more universities and colleges, so they have the chance to enter mainstream further education. Aside from Sean, who is planning to become a professional musician, I meet other successful ACE alumni, including the son of the headmaster of Maranatha School, Matthew Medlock, a graduate from Durham University who wants to work as a sports journalist. And I hear of ACE children who go on to enter various mainstream occupations, from nursing to IT - or, of course, to "do the Lord's work" themselves, like Alastair Kirk.

But I am mindful that, as a journalist, I am unlikely to be introduced to the children who lost out in this system, who rebelled against it, or who felt trapped within it. Because the question still burns about how this kind of education can possibly prepare children to make their own intellectual choices. In the US, where ACE is a much bigger force, that is really what exercises its critics. One American educationalist who is hostile to fundamentalist Christian education, David Berliner of Arizona University, has complained that in ACE schools "nearly all speculative activities about the world and the human condition have been purged from the curriculum and so, therefore, have all of the teaching methodologies that promote speculation."

A style of education that discourages doubt and debate clearly poses a question for the rest of society. As David Berliner says to me, "Their educational system is closer to ultrafundamentalism than is healthy for a democracy." Yet ACE schools are independent, they ask for no state support, and families who choose to educate their children at home do so in the face of indifference or hostility from local authorities. Aren't they just exercising their own right to free choice as to how their children should be educated? So long as their children reach a reasonable standard of learning, has anyone the right to interfere?

Ben Rogers, the associate director of the thinktank Institute for Public Policy Research, produced a recent report, What Is Religious Education For? which argued that discussion of atheism and agnosticism should be included within religious education for all children. "There is this view that parents own their children," he says. "Nobody owns kids. Children aren't yours to control, you hold them in trust, and you should cultivate certain qualities in them, including the ability to understand the value of different points of view."

The future is likely to see more of this debate, since most of the people I interviewed believed that independent fundamentalist education is set to spread in the UK, partly because of the inspiration evangelical Christians seem to take from what's happening across the Atlantic. Ben Pike talked wistfully to me at Maranatha School about the way that evangelical churches in the US have managed to bring so many children into their independent schools and home-schooling networks. "America provides us with a vision for the future," he says.

In the US evangelicals have effectively created a parallel system of education which has schooled hundreds of thousands of pupils in its messianic world view and the evangelical social and political agenda has moved into the mainstream. Evangelical Christianity is far from being such a force in Britain, but it is clearly the desire of many of those I met that it should become so. They are being inspired by the growing confidence of other faith groups. Supporters of ACE talked admiringly of Muslims who make it clear they do not wish to join the mainstream. Fundamentalist Christians point enviously to the fact that more children are currently educated in Muslim independent schools than independent evangelical Christian schools - about 14,000 compared with about 5,000 - and independent Muslim schools are growing more quickly. Rather than confronting this sectarianism with a call to inclusiveness, they would like to react with further sectarianism of their own. The goal is a more, rather than less, divided society. "Christians have been leaving it to the government to decide on their values, while Muslims have said, 'This is mine, this is my culture, this is who I am'," says Maxine Hargreaves. "Now we Christians are saying that we want to defend our culture, too. We want to take back our children."