Hi Loraine,
As others have said, provided you have sent in the deregistration letter to take your son off school roll, it really is very difficult for him to be forced back to school. Local Authorities may threaten this, but it hardly ever actually happens when parents supply appropriate information and then stand their ground.
The Facebook group itsstillgood recommended is called "Home Education and your Local Authority: Help with dealing with officialdom" and is really excellent. Some of the people who post there know everything there is to know about the law and are very experienced at helping parents to write letters if necessary to put wayward LAs in their place.
Someone on that group recently posted a very cheeky letter they had received from Medway in which the LA person wrote inviting themselves to the family home, not explaining that this visit is optional. You would be well advised to decline any such offers, especially since your son is anxious. You are well within your rights to do that, but should always answer any communication from the LA in some way.
You mentioned that you have been getting your son to do some formal academic work and that "he does sit and do the work I give him but if anytime he gets one question wrong he has a melt down saying he is useless". There are many ways to educate children. If he is finding this particular school-type approach so stressful, you could experiment with other ways. Many families find it helpful to take a complete break from all enforced learning for a few months after removing a child from school, instead exploring the child's interests and taking all the performance pressure off.
If you and your son like this approach, you can continue with it in the long run. If you decide between you that he would do better with a more formal approach then you might gradually introduce that in the autumn once he is feeling better, starting with the subjects he likes best in order to build his confidence. The process of understanding your individual child's learning needs is an ongoing one. You don't have to identify an approach immediately and stick with it. I would say that if he isn't enjoying it, it isn't right for him and you need to keep trying other ways.
You have far more freedom and flexibility than schools do. Think first about your son's actual needs, not what you think the LA would expect you to do. If you are meeting those needs, you are fulfilling your legal obligations. Then it is just a matter of explaining that. There are many other HE parents in online forums and probably in your local area who will be happy to help you figure out how to explain it in a report, so don't worry about that. Just concentrate on your lovely boy and how to make him happy. That is what really matters.