Genuine question - are there any restrictions at all on HE? Are any checks made on development, progression etc? Is there any obligation that can be enforced for any curriculum to be followed, exams taken etc? I'm sure that lots of people who HE do it "properly" but it is a bit of a concern if there is no regulation whatsoever, it does mean that some parents could just keep the kids at home all day and do nothing educational with them at all?
I've started a new topic so that your question does not get buried. The basic answer to your question is "no". Section 7 of the Education Act 1996 lays a duty on parents:
The parent of every child of compulsory school age shall cause him to receive efficient full-time education suitable to his age, ability and aptitude, and to any special educational needs he may have, either by regular attendance at school or otherwise.
It is up to a parent what form the education should take. The big problem with the checks you suggest is that children's learning does not progress along fixed lines. As a sociaety, we do not agree on what we mean by an education (for me, five GCSEs at A* to C at 16 does not necessarily mean a child has received an education suitable to A, A and A).