Firstly, something that really alarmed me was that you think you just eat very little, and yet no one knows, and you chuck food away, which makes you anorexic in my mind.
Don't try and do DofE whilst anorexic, you won't manage it (Bear in mind, I know what you're going through, was anorexic myself whilst wanting to do my DofE)
Trust me, by the time you get to the second day of the expedition, you're usually starving, even if you are eating! So please make the effort. Start eating again now, be really disciplined with yourself and build up your claories each day to the recommended resting 2000/2500. The 4000 calories you are reccomened to eat should then come easier and your expedition will be a success.
Good Luck.