manky - I became interested in this in my last job (research post) and did do a little bit of research into it. I actually wanted to base my PhD on it but as I was working in a teacher training college they were understandably not too keen on this! As the programme may have revealed (I didn't see it) it is not, contrary to popular belief the law to send your child to school. You must demonstrate that your child is receiving an education and this of course can be done at home. Many homeschoolers work in a cooperative with other families which means that they can share resources and the children socialise with each other. Homeschooling appears to be more popular in America probably because of the size of the country and there being many very rural places. Other reasons for homeschooling are on religious grounds. Other families have kids who just don't adjust to school either because they are very shy or are being bullied. Or of course the parents just want to control what their children are learning and perhaps expose them to a more flexible curriculum.
Homeschooling is a lot of hard work for the parent. You don't need to be qualified but obviously a good general education is requried. I am no expert in this but there are many organisations around. I don't know how homeschooling fits into national exams, but there is no reason why a child couldn't sit them if they had done the coursework. I can dig out some info or you can do a web search and find out information that way. Also the Internet itself is a useful resource for teachign materials and there are websites designed for this.
There are many different models of teaching and learning which are being used more often. For example travelling families such as those who work in circuses can still be educated by means of laptops and logging onto a remote tutor. We have the technology (I sound like Dr Spock!) and therefore it is possible to learn without necessarily attending a physical building.