This is simply untrue.
Most families living solely on UC in the UK are officially living below the poverty line. UC is designed to lift people out of poverty, but many, many families on UC, particularly those with more than two children, struggle to afford basic necessities.
All developed countries and many developing countries now have a problem with childhood obesity. The highest rates are among Pacific Islanders, Chile, and in the Middle East - Kuwait, UAE and Qatar.
"In season fruit and veg are cheaper than takeaways"
Calorie for calorie the cheapest foods, by a very long way, are processed foods with a lot of sugar and fat.
If you live in a food environment where there's mass availability of comparatively very cheap, highly palatable foods - ie, those with lots of fat, sugar and salt - the groups experiencing the highest levels of social stress are more likely to become obese.
I know you want obesity to be seen as a moral failing, or a failing of education, but obesity experts know it's far more complex than that, and requires regulatory and social change, rather than moralising and finger wagging, which over the years have proved to be a singularly unsuccessful strategy of addressing the ever increasing obesity rate.