I think the way she held her drink suggested alcohol dependency. At least it reminded me how I used to, gripping it tightly, almost huddled over it like some precious commodity.
But yes, the overwhelming thing was her depression. Not that that was a bad thing because she was a depressive first and an alcoholic second. My problem was the same, although I suppose it's an individual experience that no two people share EXACTLY.
And I still maintain her accent was gash. I've heard some English actresses do it well. She wasn't one of them. However I still maintain overall that it's easier for Americans to do English accents than vice-versa. Why, I don't know, but I think it's true.