In England children who are educated at home are deemed to be ‘home educated’. Those who follow an unstructured and child led approach call it ‘autonomous education’.
In the USA children are ‘home schooled’. And those who follow an unstructured and child led approach call it ‘unschooling’.
I like the child led approach. It shows respect for the child. All children love to learn, but not many like to be taught. There is a world of difference in those two concepts.
Here is a great video introducing the concept of educating at home.
School is not compulsory in Britain by education is.