Good point. I've long given up on the Horniman Cafe because of that.
I know they put on various evening events but no idea if they were also selling alcohol. Presumably they have some sort of restricted/temporary alcohol licence to cover weddings in the summer months.
However the lack of parking is a real problem and the number of people attending these events has to be carefully controlled. No matter how much people would like it to be so, I don't think the Horniman is the right sort of venue to stage huge events. That's just a fact.