I agree. It can be difficult to be sure you have the correct information, and you are wise to want to check that. If you go to a big national home ed website, they will have accurate information.
First make sure you get advice for the relevant country. Education is devolved, so the law is slightly different in each of the countries of the UK. Scotland is the only one where you cannot immediately deregister upon demand to home educate. There, you need to obtain the consent of the LA first, but that should be a straightforward and quick process and there are few grounds on which they can refuse. Also, if your child is being educated at a special school, you need LA consent. (This is true even of independent school if the fees are paid by the LA.)
If ever you are unsure, ask people to direct you to the actual law. Most of the template letters you will find online quote the legislation, which you can go read for yourself. Assuming you are in England or Wales, you will see that there is no reference IN LAW to any requirement for meetings with the LA, or for you to inform the LA directly of your decision to home educate. Therefore there is no such requirement. Given that you are not requesting any service from them, bureaucrats at your LA do not get to make up policies and demand your compliance. If your LA tries to insist you must do xyz, just write to them and ask them to cite the law which says you have to.
Home education in itself is not a safeguarding concern. Even the government, which has often viewed HE with suspicion, acknowledges this. As long as you have told your independent school that your child will not be attending, their role is finished. Obviously if they'd already had serious concerns about your child's welfare due to any previous incident, they would have made a referral to Social Care when that happened.
These are the biggest home ed organisations in each country:
England/Wales: https://www.educationotherwise.org/
Scotland: https://homeeducationscotland.org.uk/
NI: https://hedni.org/