some negligible minority - a small fraction of home educators who are, themselves. a small fraction of the population
This is very interesting. The problem is that nobody really knows how many children in this country are not attending school. Most experts believe that universal literacy in this country was attained by making sure that almost every child was in school. The fear is that if a significant proportion were, as was the case during the nineteenth century, to be out of school, then things like illiteracy would begin to rise.
So readers are right in one sense; if the numbers of children who are not at school are indeed tiny, then this will hardly affect the country's literacy rate or academic achievement in general. However, some researchers who are widely respected in the world of home education are making increasingly extravagant claims about the scale of the phenomenon. Paula Rothermel, for instance, is currently saying that she believes that the number of children in this country aged between five and sixteen who are not at school now runs into the hundreds of thousands. She claims to have identified between 300,000 and 500,000 such children. Yes, you did read that correctly; that's half a million children who are not at school. If this were to be true, then of course local authorities might well have cause for concern.