Many parents have withdrawn their children from schools to protect them from malign influences: the de-motivating effect of institutional life, the exposure to unsavoury peer groups, drugs, sex, bullying and delinquency.
It is, however, the growth of new technology and life-long learning that will cause many more families to reject mainstream schooling, Professor Hargreaves says.
"Schoolteachers were once needed in part because they knew more than the parents and what they knew was not readily available from an alternative source," he says. "Neither condition now applies for many homes."
National curriculum programmes of study and exam syllabuses are now available and they will become increasingly accessible through the Internet and its successors.
Furthermore, in the near future more than a third of the workforce will be home-workers and teleworkers who make only occasional visits to their company's offices.
Such parents will realise that schools are among the last organisations to change, but will eventually share the fate of factories and offices. They will supervise (rather than teach) their children at home, working and learning together.
There will then be no pressure to live near a "good" school, and valuable time and money will not be wasted driving children to and from school through peak-hour traffic.
Home-schooling parents who do not wish to be distracted from their own work will form corsortia, with each parent looking after the children from several families for one day a week. These family consortia will also contract out some of their teaching work to a new style of peripatetic teacher who makes a career and an income by moving between families for a few hours a week.
"Teacher entrepreneurs will also arise, buying up redundant schools to offer home-schoolers selected curricular features not easily provided at home - practical science, athletics, the performing arts - as well as opportunities for students to mix with their age group," Professor Hargreaves predicts.
"So students will attend school on one day a week and for a specific purpose - which means far fewer schools, with their huge capital and recurrent costs, will be needed."