I think it all but requires some existing, quality-valuing food culture. Try to serve good lunches to kids here and you'd have all the parents crying about how their kids "can't" eat that and need an Uncrustable and chocolate milk instead or whatever.
One challenge in the UK, especially somewhere like London, is we have a fair amount of diversity in food choices.
Providing nutritious, tasty meals on a very limited budget with options for vegan, vegetarian, kosher, halal, gluten free and other diets can be a challenge for schools, and many primary schools are quite small without cooking facilities. When I was young, it was normal in primary to bring a "packed lunch" from home, usually a sandwich and crisps. The standard UK lunch as an adult is still a sandwich for most people. The move towards free cooked school meals has been suggested because turns out that many don't have access to a daily healthy cooked meal at home.
The normal response to that is to use a contract or municipal service to bring in hot food. It's usually municipal.
However we had decently cheap lunch, and above all even cheaper breakfast provided by the Petits Déjeuners, for which I am very grateful.
I only realised later that my parents struggled at times, and that those were lifesavers for them.
https://imgur.com/a/8KECVAp