If I am remembering the stats correctly, we were healthiest as a nation post-war. There was a high ratio of jobs with physical activity, a lot of vegetables being eaten and less meat, and a lot less sugar.
The chances of getting back to that are minimal at this point, but if could be moved that way with work and education.
Any rich country tends to have a surfeit of food available for it's population, and we are a rich country without a doubt. That is not to say there aren't deprived and poor people of course, just that cheap crappy food is more available than say Mozambique or Papua New Guinea.
As mentioned above, food size portions are large, and people move less and eat more.
The Chief medical officer has no tax raising powers, that's beyond her remit or authority, but she does have influence.
My dislike of the "Nanny state" approach that this thread is about, is the general derogatory, patronising attitude that governments cal fall into. They may decide that the public is "stupid" or "ignorant", but it was their job to educate them in the first place!
Taxing "bad" foods merely removes money from people who are already hard pressed when it comes to money, and always seems to move the money to people or organisations/businesses that are already rich and only getting richer.
Education... education... education. That is the only longer term approach that will work. Anything else is just rearranging deckchairs on the Titanic.