Sadly you can only do what you can do. It's normal to feel like you should be doing something, but as a parent all you can do is love them and support them. Which I'm sure you are doing anyway. Recovery has to come from inside them, so the means such as doctors and dieticians are important, but their desire to get better is paramount.
The place in north london is called Rhodes farm, and is extremely strict, but has a high success rate. Expensive though.
The bingeing story reaches home here, as Mum and I often had to pick up the peices after my sister would binge and purge. No, of course you can't deny her food, but perhaps make nutritious, high energy meals, and make a certain amount of food available to her, but lock up the remainder, as she can't go on draining your bank balance. Maybe she will learn that that is what is there, and no more, so if she does want to eat, she should eat with the family. If she purges, then sorry for being course, but at least it won't be so much wasted food as if she raided the cupboards.
Again, I am so sorry for what you are going through. No Mum should have to see their child starve. But take it one day at a time, one minute if neccessary, and let her see you as a friend, not an enemy, or someone to manipulate.
Keep talking to us! xxx