Sorry to hear what your daughter and family are going through.
I had bulimia myself in my late teens early 20s, actually if I'm honest I had relapses right through my 20s. I am now mid 30s.
The NHS assistance offered to me was a CD Rom self help programme which I found useless to be honest. I believe I was also offered to attend group sessions but at the time, I couldn't think of anything worse and didn't go.
Whilst my family knew what I was going through and my mum came with me to get help in the first place, I felt like it was completely ignored and not really spoke of. I'm not saying I would have wanted open conversations about it but I would have appreciated open questions asking how I was or if there is anything they could do. The answer would have probably been no but I wouldn't have felt so alone. On that note reassurance that you are there for her, she is loved etc. is important. I would avoid any comments about her appearance etc. Also no criticism, my sibling would criticise me and it just made the way I felt worse.
One insight that I didn't learn until years later is that bulimia can be an outpouring of emotional trauma and attempt at achieving some sort of control in an environment where the individual feels vulnerable. I grew up in a rather unstable family and this made so much sense to me learning about it years on, I had thought it was just about wanting to be thinner etc but it was so much deeper than that. Has your daughter been through any emotional trauma/instability? If so, I would ensure any counselling is dealing with that potentially as a route cause. It also helped me in later life to hear that what I was going through wasn't my fault, I wasn't 'broken'.
On the days she isn't eating try and encourage her to eat something even if small but don't push too hard. Binging is a vicious cycle and made worse by not eating inbetween because being hungry might me more likely to trigger a binge. However it might be helpful for you to understand that whilst binging, at least for me, it's hard to control yourself, it's a bit like a addiction then once is done, a feeling of disgust ensues and vomiting gives a real sense of relief.
There is a book called over eaters anonymous that is aimed at assisting with eating disorders, you may also want to speak to a therapist yourself to see how you can help.
This is a bit of a brain dump but I hope it is of some use. It is of course from my own personal experience and everyone's case will be different. Love to you and your family, especially your daughter x