I have a teenage daughter myself and know what you mean! That must be so difficult for you.
Living with an addict, I understand how hard it is to feel so helpless, it sounds like you’re being as open and available as possible without judging her or being angry with her which is positive.
It sounds like she wants help so maybe you could look for an alternative alcohol service in London where she is That is better than the one she’s already been to. Some are better than others!
I wish you all the best and hope that you can get some help from someone who’s been in a similar situation