Home education is perfectly legal in the UK; education is compulsory, going to school is not.

Section 7 of the 1996 Education Act applies to England and Wales, it says that:
"The parent of every child of compulsory school age shall cause him to receive efficient full-time education suitable:
(a) to his age, ability and aptitude, and
(b) to any special educational needs he may have, either by regular attendance at school or otherwise"

Home education is one of the "otherwise" options.  It is perfectly legal, requiring no special teaching qualifications.  Families do not need to follow the national curriculum or adopt any particular methodology.  This allows families to respond to their children’s educational needs in a personal way that best suits the individual.  Home education breaks away from the ‘one size fits all’ approach and allows children to learn in a more natural way, responding to what interests and inspires them.

The processes and guidelines do vary though in different parts of the UK.  These are the EHE Guidelines for Local Authorities in England: