Schoolhouse Home Education Association's application, encouraged by the previous government, was turned down last week by Brian Wilson, the Education Minister, on what Mr Wilson termed "a matter of principle" - that state education is available "free of charge to all".
But Alison Preuss, secretary of Schoolhouse, protested: "The Government fails to see that free for all does not mean suitable for all, and that school is not necessarily the same as education."
According to the 1980 Education Scotland Act, parents are charged with the responsibility to "provide efficient education" for their children suitable to their "age, ability and aptitude" either by sending them to a state school "or by other means".
Parents who chose home as their "other means" receive no state support but are subject to inspections by a local authority. "There is still a relationship with these authorities so some public expenditure should be afforded," Ms Preuss said.
Since it was set up a year ago Schoolhouse has been joined by more than 200 families and says it has an increasing volume of enquiries from parents, many "desperate" because of problems their children are facing at school.
Ms Preuss says these include bullying and disputes over special needs entitlements. Schoolhouse is an offshoot of the UK-wide organisation Education Otherwise, which estimates that around 50,000 children, 1 per cent of the school-age population, are home educated.
Roland Meighan, professor of special education at Nottingham University, says: "The academic excellence of home-schooled children has been repeatedly demonstrated in research in the United States and in England and Wales. Social and emotional scores are sound, too."
The experience of parents in Scotland who educate children at home also provides "overwhelming" evidence that it can be beneficial, Ms Preuss claims. "Everyone who has done it says what a difference it makes to their own lives and those of their children."
She teaches her three children, aged eight to 13, at her home in Dundee. The Scottish Office cash would have helped to set up a centre in Dundee providing a helpline manned by trained staff. It would also have provided resources such as books and equipment, Ms Preuss says.
No home education organisation in England receives public funding. Professor Meighan says: "In supporting only mass compulsory education the Government are perpetuating an obsolete system, despite the arguments put to them."
He argues that home education will grow in line with advances in technology and home-based working. "Home educators are not the dominant teacher, as happens in schools. They can operate as learning site managers allowing children to learn independently within agreed plans."