Cookery lessons wouldn't be controversial unless you made them compulsory (which probably wouldn't be necessary anyway) or if you just included them as part of secondary education (as quite a lot of the more profitable private schools do). If they were implemented like that, I can't really see any problem that the bulk of people would have with them.
As for your proposal that the government ban fast-food outlets, not only does government control of the national diet smack terribly of totalitarianism (which you seem to lean towards anyway) but it also flies in the face of the simple, ugly, but undeniable fact that people do like fast food.
Yes, there are a lot of people who just eat it out of convenience or for budgetary reasons (I'm not going to talk about majority/minority ratios), but there are a helluvalot of people who eat it because they like it. And no, they're not brainwashed into it either. They like it. Plus the fact that - like most things - it's pretty harmless if consumed in moderation and this is where the problem lies for a lot of people.
Thus it's really a matter of education. Which is kinda what you proposed.