No, if a child is not a registered pupil in a school, you do not have to inform anyone.
Many home educating families stay unknown, all the way through their child's compulsory education.
There are a number of webpages-we have a thread about 'Websites about Home Education which lists lots of helpful places for you.
We've got one too called Books about Home Education too.
Most home educators I know, don't limit themselves by sticking to any sort of curriculum, there are so very many interesting things to learn about, there is no set list of things 'you should be covering'
The Department of Education has set out "Elective Home Education :Guidelines for Local Authorities" that are worth reading I think, as they set out what the LA should be doing, and what the limits of their powers and responsibilities are.
For example, it lists in Section 3.13:
Home educating parents are NOT required to:
teach the National Curriculum
provide a broad and balanced education
have a timetable
have premises equipped to any particular standard
set hours during which education will take place
have any specific qualifications
make detailed plans in advance
observe school hours, days or terms
give formal lessons
mark work done by their child
formally assess progress or set development objectives
reproduce school type peer group socialisation
match school-based, age-specific standards.
hth