I was waiting for someone more knowledgeable to come along, but I don't want to leave your post unanswered for long!
My understanding from hanging around on HE forums is that the LA is obliged to maintain the EHCP, whether the parents want it or not, unless it is quite clear that the EHCP is no longer needed. They have to conduct annual reviews.
This doesn't mean they have any "hold" over you. The EHCP is somewhat inconsequential for children who are HE, except in those cases where the LA has actually agreed to provide something - which I guess is rare. It doesn't specify what provision YOU have to make while home educating, only what the LA has to make if you've asked them to educate your child. I understand that maintaining it will make life easier if you ever do want to send your child to school or college.
Here's a website which should help: ehe-sen.org.uk/annreview.php I'm sure Fiona (whose website that is, and who posts on this board) will be able to help you out if you have questions. She's very well informed.
And here is a Facebook group which also has tremendously helpful and knowledgeable members: "Home Education and your Local Authority: Help with dealing with Officialdom". This is mainly for people who are getting hassle from their LA, but also handy for situations such as yours.
Good luck, and I hope the home education goes well for you!