Living through ED has to be soul destroying for you and I sense you are caught in a dilemma between what you would wish for and what is reality. Your CAMHS therapist will probably say very little because this is about you, and you have to realise that this is your life and your decisions. You are in control. It matters not what others think, our say or do, you have to reconcile with yourself a course of action that sits well with you. The reality is you are not well enough to continue your studies to the standard you want. You know that and your parents know it too.
If you had a physical injury what would be your response and how much time would you need to recover? Why has food become the vehicle for such a representative issue for you? How did you end up so unhappy at school?
You talk about being a high achiever? You still are and always will be. Nothing has changed there. This is your psyche having a rest. If you were a pressure cooker your safety valve would have blown. The stress and pressure trying to get the best grades ever are phenomenal. It can seem all consuming and there appears at times to be no let up or no way out. There always is a way most definitely, and it has to be the way you choose, that is right for you. But finishing exams and study does have an ending one day soon, particularly in Year 13 The short time can be so intense, so mentally painful with no time to breathe. It's a bit like swimming underwater for far too long.
Why don't you go and have a chat to your tutors or year heads if you are able to find out what time frames and options you have? Ignore the fact you hate the place just see what options and opinions they have. You wouldn't necessarily lose the option to study at Cambridge even if you were to miss a year. Why is Cambridge so important to you? Why is it the be all and end all and who says so? Where would you like to be in 1 year, 5 years, 10 years time? Your mental health is as important as your physical health. Sometimes it is important to learn how to cope with pressures, to prioritise, to clean slate, to shut off etc and to have sanity and pure peace of mind. This too is a learned life skill. Sometimes there is no perfect day and no perfect answer, just that you have done your best.
Maybe taking a year out would give you time to decompress and give you perspective? You can stop right now, get a better outlook on life and if and when you are ready just start again. The hardest part is seeing your friends swan off here there and everywhere. You could spend a year quietly studying the course content with no time pressures ready for your final year and be one step ahead. You can then smash it out of the park.
No one says you have to return to a school you clearly hated. A new environment, a new set of faces in a different college can be a whole new start and make you feel you are at ease again. The trick is to learn more about yourself, learn how you deal with pressure, how you cope. There will always be some learning from every hurdle in life, from every experience. There is more learning from failure and how you cope with it. It takes more courage to pick yourself up and to recover. Only you can decide how burnt out you feel. Try using the MIND web site to chat and get support and I hope you can find your confidence and your way forward whatever you decide to do.