I am very sorry to hear about your daughter's anorexia. It's such a horrible, frightening illness.
I wondered if my experience may help a little? You mentioned that she has depression too, and it is a viscious circle with both depression and anorexia.
I had anorexia as a teen, and managed to get counselling for it after three years (not much support until then unfortunately).
However I did revisit anorexia again recently (now aged 39yrs) because I started counselling for other things, and that triggered the anorexia as a coping mechanism. It was an enormous shock from being able to eat and enjoy food enough, to being frightened of even looking at it, cooking it was horrible etc etc.
BUT someone suggested that I get help alongside the counselling. So I went to visit a highly recommended lady who is a spiritual healer. I did go with an open mind, and she is a lovely lady, very grounded actually!
Within the one hour session, I felt serene and calm. Over the next few session she somehow managed to break the cycle of depression and eating disorder. And more importantly to break the association between food and emotion.
She encouraged me to get outside, to stop hiding from the world and to show my emotions (hard!)
But really the main thing was her healing technique. It was non invasive, relaxing AND IT WORKED. I feel so much better.
This was only eight weeks ago btw. And I am still having counselling, but feeling much more in conrol of things.
I don't know if this is useful at all, but it may be worth thinking about this kind of approach? I highly recommend it, of course.
Oh, and when I was feeling really poorly, I would actively look for tv programmes with anorexia so that I could compare the illness and body shape, and also to feel that I was not alone with it. But now I am better, I have no interest in looking, it just doesn't figure. So from my point of view, watching such programmes didn't make my anorexia worse, because I couldn't possibly feel any worse than I did. The programmes actually were quite comforting, because I was not facing the illness alone iykwim. I needed to feel that I wasn't going crazy, because the thoughts running through my head seemed very crazy. That of course is a personal point of view, it may be very different for an impressionable teenager.
And I agree wholeheartedly with the part of the C4 programme with Anna, who is a good shape and in good health. She really does not help anyone struggling with ed, she makes me feel quite angry with her views of her body and how she feels she "needs" to change every bit of it - she should be teaching the viewers that body shape/size is irrelevant and to be proud of what you look like.
I hope that all made some sense, apologies for rambling.
I hope your daughter gets the help she really needs from her gp etc.