Please don't follow Icantfinda freenickname's advice, but take advice from people with experience of Home Education
As far as I can tell from people I know IRL and online, LA involvement is a hassle and very very rarely something Home Educators find valuable for themselves in any way.
"they have to be sure you are actually educating your child, not just keeping them out of school.". No. They don't. THe legal responsibility for educating a child rests with its parents, who may choose to exercise that responsibility either by sending them to school OR OTHERWISE. If LAs have reason to believe that an education suitable to the age, aptitude, ability and any SEN of the child is NOT taking place, then they have a legal responsibility to investigate. But they have no legal remit to assess, regularly or otherwise, the educational provision offered to every child (which is a damn good thing for the mainstream, or there'd be a hell of a lot of schools facing prosecution for failing in their duty).
Callisto - I think lots of people apply to more than one school, and then when they get a place at the preferred one, they turn down the place at the non-preferred one. Or they decide to go private instead. All you would need to do would be to write to them saying "gosh, thank you for the place but we have decided to make private arrangements for our child's education". Bam. And no need for anyone to know whether that means you're going private or HEing or... exercising your legal right not to be educating your child at all until the term after they become 5 (obviously, you'll need to keep them locked in a cupboard 24/7 to actually stop them learning like a little sponge, but I'm sure you could manage it if you really worked at it). Even if you are on a list, the LA have no business being in touch with you in any way until the term after they become 5, and if they try to get in touch, you can tell them where to shove it. Politely.
(I'm feeling really agressive today. Third trimester-itis)