How, when and if you need to deal with the local authority (LA) with regards to home-education depends on your situation.
If your child has never been to school, there is NO obligation to inform the local authority of your intention to home-educate. You simply do not apply for a school place.
If you have applied for a reception place but have changed your mind, you need to withdraw your application or your acceptance (if you have already accepted a place).
If your child is already in school (not a special school, as below), then you will need to deregister your child from that school.
If your child is in a special school (this includes an independent special school arranged/paid for by the LA), then the parent(s) need to seek consent from the LA to deregister.
If your child is in an independent special school that is arranged and paid for by the parents, consent from the LA is not required.
The government guidelines for local authorities with regards to elective home education can be downloaded here. The guidelines for parents are here but it is worth being very familiar with the aformentioned local authority version.
Section 7 of the Education Act 1996 applies to England and Wales:
7 Duty of parents to secure education of children of compulsory school age
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.
Home education is covered under “education otherwise” and ensures that every parent has the right to chose not to send their child into the state schooling system.
The rights of a parent to chose their childs education is also further enshrined in the Universal Declaration of Human Rights which says “Parents have a prior right to choose the kind of education that shall be given to their children” (Article 26, para 3).