In England and Wales the Edication Acts make it clear that while education is compulsory, school attendance is not.
Parents (or the person who has care of the child) are responsible for ensuring that their children are properly educated but it is their decision whether to use schools or provide education at home. However, if a child of compulsory school age is registered at a school the responsibility of the parent is to ensure that the child regularly attends school.
And to answer north star's point, if the LEAs suspect that "a child of compulsory school age in their area is not receiving suitable education, either by regular attendance at school or otherwise, they shall serve a notice in writing on the parent requiring him to satisfy them within the period specified in the notice that the child is receiving such education." This means that parents answer to the Powers That Be, not vice versa.