Firstly, I wouldn't ban packed lunches and I don't believe the figure of only 1% meeting nutritional guidelines. At my GD's school the meals are not very nice and frequently served half cold. I do think many children do have dreadful packed lunches, combined, I imagine with poor nutrition at home. School meals should be improved to the point where children want to eat them and this will need more than the paltry amount that is spent on ingredients by some of the suppliers.
This is what I think needs to happen.
There needs to be a massive, sustained public education campaign. The food industry needs to take some responsibility, stop selling crap at cheap prices, and promote healthier foods. Advertising of fatty and sugar-loaded drinks and foods should be banned. Politicians and their "advisers" should be obliged to declare and then renounce links with the food industry. Supersizing in the food industry should be banned. The DT curriculum in schools should regain its emphasis on preparation of food, budgeting and cooking. The poorest families should have access to the equipment they need for cooking. Schemes to teach people how to cook simple, healthy food should be developed and supported.
Any initiative that encourages the growing and cooking of fresh food should be supported and encouraged. Allotments should be protected and used (there are still empty ones in many cities). All this would cost money but eventually bring savings in health, welfare and education budgets.
Finland managed to do it.