While not everybody who gets a little drunk in a heartbreak is an alcoholic, alcoholics are not all fall-down drunks who drink bottle after bottle either. As I understand it (with the caveat I am not a medical professional, psychologist, or any other sort of expert), an alcoholic is someone who, in some part, feels a NEED for a drink, that they can't get past a moment or a day, or cope with a certain emotion, or sleep or what-have-you, without it. Whether that's one drink a night or several at any time is irrelevant--it's the compulsion to drink, or reliance upon drinking as a coping mechanism. In fact many alcoholics try to fool themselves or their family/friends into believing they are "in control" because it's "just one drink" at a time, even though they are letting "that one drink" compel them.
Trixie is shown to be a probable alcoholic because a) she herself says she wants to stop and feels she can't/needs help doing so (and that's the biggest reason right there), and b) even before her "rock bottom" binges, they've shown her several times hesitating and then reaching for a drink, like she knows she shouldn't or doesn't want to but feels compelled. I think the portrayal of Trixie as an alcoholic is actually pretty realistic and the problem is that realism is seldom seen on TV and other pop culture media. Contrary to popular belief, substance abuse is seldom an "obvious" thing and people who suffer from it also often do a very good job for keeping it under wraps and/or convincing themselves and others their behavior is "normal" for a long time. Alcoholism can particularly well-hidden because of this because it IS also a social activity and there indeed ARE people who can have "that one drink" but not be addicted. I'm actually really glad "Call the Midwife" portrayed it the way they have because maybe it'll open some people's eyes that alcoholism and similar issues can develop and reveal itself in that way.
New here so hope it's okay to just jump in like this. Love this show and have been reading all of y'alls insightful comments for awhile and really enjoying them.