Lesley, can you tell us a little more about your relationship with this person? Is she family, or friend? I ask because who she is may affect how much help you can get for her.
What do you think her problems are? You say 'mental health' but do you know what kind? Has she been mentally ill for long? Is this 'sudden'? Is she having any kind of treatment for it?
You say you've 'asked if she can go into hospital to be assessed' - who have you asked? Her GP? Other members of her family?
If she hasn't been to her GP, then the GP is really the first port of call for her. But if she has already been to the GP, I would think it is the GP who should have referred her to a psychiatrist for assessement, or simply sent her for counselling or therapy (or put her on pills).
However, it is all too often the case that someone who is mentally ill does not acknowledge they are mentally ill, and/or refuses either to seek help, or to accept any kind of treatment at all. (As I said, she may be 'self-medicating' on alcohol anyway??)
What is it you would like for her? Do you think she should be in a psychiatric hospital? Do you think she needs counselling or therapy? Do you think she should take medication?
Do you simply think she should stop abusing alcohol? If so ,that may be the hardest of all to achieve! Most substance abusers find it VERY hard, if not impossible, to give up.
Do you think she is 'so bad' that actually she needs to be sectioned, and placed in a psychiatric hospital without her consent, if it comes to it?
Mental health is ALWAYS very difficult to deal with, and if alcoholism is added in, that's even more difficult.
You sound a concerned friend or family (whichever you are), and it's good she has you 'looking out for her'.....but it may not be what she wants alas. She may not cooperate?
What does she say she wants? Does she say she wants help? Or just to be left on her own to get on with her drinking???
All VERY difficult alas.