There are a range of things they could do but I would go further than voluntary agreements. Maybe ban advertising and make any drink or food judged to be over an unhealthy level of refined sugar be sold with cigarette style labels - name of product, health warning and pictures of Shane McGowan's teeth or a diabetic ulcerated foot or similar. Diet drinks could be labelled similarly but with warnings they are full of chemicals that will make your appetite go haywire and probably give you cancer. In other words let people have the unpalatable truth about it at the point they consume it.
Yes, I'd go with that idea.
As it happens, I don't think you'd need to go that far.
If the Food Standards Agency introduce compulsory front of pack 'traffic light' labeling (they've been discussing it back and forth for years now, for fat, salt sugars etc, though not for things like artificial sweeteners, which perhaps should also be considered, as you say), manufacturers would begin to self-regulate.
Most manufacturers and retailers don't want their products to be flagged up quite so overtly as "BAD", and will begin to change them accordingly. (Sainsbury's, for example, do have voluntary front of pack traffic light labelling on most of their own brand products and, when they first introduced it, they actively changed many of their recipes so that they fell below the 'red' thresholds).