They try to advise against drinking on anti ds just because, as you say, alcohol counteracts the effects of the antidepressants, apparently. I have not found this, and have spent many years with fewer hangovers and the accociated guilt. Obviously not drinking enough
The NHS loves CBT because it is defined, short, and therefore relatively cheap. It really is worth asking what other kinds of therapy is available.
This is the Drinkulator which may help you assess how much you are actually drinking.
Also it is worth remembering that a binge is a binge, and you can as well binge on a dry biscuit as you can on a bottle of vodka, although it's harder to see why anyone would want to deny themselves a dry biscuit.
If you are using booze as a stick to beat yourself up with, it is important to learn not to before you become dependent.
This is pretty rich coming from me.... I am learning.