“To people like Jamie Oliver, my dad would look lazy or like a bad parent, because we had days where all there was on offer was toast and crisps.”

This is what Kat Bukowicki, a 22-year-old from Leicestershire, told me after I saw her talking about the subject on Twitter, and asked for her story of facing food poverty when growing up.

“My brother and I took multivitamins as we couldn’t afford fruit, and I remember there were some meals that were just whatever had been reduced that day. For one of my birthdays I got £10 from a relative and spent it on fish and chips, not just because we deserved a treat, but because there was literally no food in the house.”

From the age of six, Kat was looked after by her father. Her father worked full time on low wages. Like many parents on or near the poverty line, he would sometimes go without food himself. Moreover, according to Kat, he “simply did not have the energy to cook a super healthy meal every night” for the two young children he had to raise.

It’s hard to see how this situation could be helped by new proposals from the celebrity chef Jamie Oliver and the Scottish first minister Nicola Sturgeon. They want to tackle childhood obesity by treating it as a marketing problem, banning special offers on unhealthy food. But Kat’s father wasn’t in information deficit, unaware that fresh fish and broccoli were better than frozen pizza. Kat puts it bluntly: “If ‘junk’ food was made more expensive when I was a kid, sometimes we would not have eaten at all.”

Since the proposals hit the news, the pushback has been fierce, with many people making a simple point: if you want to get people to eat better, don’t make bad food more expensive – make good food cheaper. But that seems so obvious a solution it’s worth asking why so many people would need to point it out. Why do we, as a society, approach public health from a punishment point of view rather than trying to increase accessibility?

Partly it’s down to simple classism – a deeply rooted belief that the poor are feckless and make bad choices. But beyond that, even among those who accept that there are structural components to poverty in the UK, we have become trapped by an approach to public policy that takes the most obvious solutions off the table before we even start considering the problem.

The Scottish Public Health Observatory carried out research that said the best results came not from specifically targeted interventions, but from broader social reforms aimed at increasing incomes and redistributing wealth. It’s hardly counter-intuitive to suggest that people with higher incomes, shorter commutes and more leisure time will have more freedom to eat and live better. Even in the demographics that aren’t struggling to eke out the maximum calories from their last fiver, there can still be significant structural barriers to healthy lifestyle choices.

Her father wasn’t in information deficit, unaware that fresh fish and broccoli were better than frozen pizza

Structural reform would also have a big impact on the growing mental health crisis. Poverty and poor mental health are interrelated, although it’s rare to see this addressed in policy. The stress of low incomes and insecure work has a negative impact on mental health, and poor mental health often acts as a barrier to improving one’s lot. And of course, the worse your mental health, the less energy you have to eat well. Living on capitalism’s knife edge is bad for you – often in ways that make it more difficult for you to make the bad things better.

We shy away from policies that would address these broader structural issues because we have become more terrified of the negative outcomes of government interference in markets than of the negative outcomes of government inaction. We run scared from policies that would increase wages and leisure time, because “the economy” might suffer – as if it were an angry volcano god to be placated with human sacrifice. We have “reformed” the welfare state into tatters because we think it’s more important that absolutely nobody gets a penny more than they “deserve” than it is to ensure that everyone has the capacity to eat and live well. And while the Tories are all over the idea that reducing tax will leave people with more money in their pocket, they often seem blind to the fact that for people with low incomes their rent and bills eat up a much bigger proportion of their wages than tax.

What’s left for policymakers? Mucking about on the edges, pilot schemes and programmes to nudge or price people into healthier choices. None are going to work unless we alter the structure of society and make these choices accessible. It’s time to stop trying to fix the symptoms of an unhealthy society – and start treating the causes.

• Phil McDuff writes on economics and social policy