It's the story with everything: food, health, class and one of the country's biggest celebrities. Four years ago, Jamie Oliver launched a hugely popular campaign to banish junk food from school dinners; out went burgers, chips and fizzy drinks, and in came jacket potatoes, fresh fruit and yogurt. Oliver's television series Jamie's School Dinners was widely praised, and the Government came up with a £627m healthy-eating initiative for schools. Take-up of school dinners, which fell below half the nation's schoolchildren as long ago as 1984, was expected to rise as parents seized the opportunity to improve their kids' health.

Sadly, it hasn't turned out like that. Last week it emerged that there's been a small increase in the number of children eating school dinners in some areas, but nowhere near enough to meet the Government's target of half of all pupils nationwide. Sixty per cent of primary-school pupils are avoiding school dinners, and among older children it's two-thirds. In some parts of the country, take-up has actually fallen since the healthy-eating initiative began, leading the Lib Dems to claim that 400,000 fewer children are eating school dinners.

Even if that figure is an exaggeration, the overall reaction is hardly a ringing endorsement of the efforts of the Government or the TV chef. What people eat as adults tends to be decided by the meals they eat when they're growing up, and another set of statistics published last week confirms a significant North-South divide. Families in Scotland and the North of England buy more crisps, processed food and chips; they are fatter and die earlier than people in the South, who spend more money on fruit and vegetables. In Stockton-on-Tees in the North-east, one in six children starting school is already clinically obese, compared with only one in 25 in West Sussex.

This suggests either that substantial numbers of people ignore health education campaigns or – as some campaigners have claimed for years – that they have developed what amounts to an addiction to junk food. When Oliver began his school dinners campaign, some mothers in South Yorkshire responded by delivering takeaway food over the wall to children who didn't like the healthy alternative on offer in school. Oliver was so angry that he started cookery classes in Rotherham, showing sceptical locals how to prepare nutritious meals and celebrating several high-profile conversions to healthy eating.

But a report last week from the Association of Public Health Observatories shows how far there is to go: Rotherham is worse than the national average on 27 out of 31 indicators of public health, including obesity in children and adults, life expectancy and binge drinking. It's also poorer, reflecting the central role of class in determining what people eat and the state of their health.

Junk food is a killer. So is over-eating in any form, and not getting enough exercise. Most people know this, even if they're not aware of new research which appears to confirm the health benefits of a dramatically restricted diet; under-eating seems to protect against cancer and cardio-vascular disease, and slows the ageing process in monkeys. But advising people to embark on a calorie-restricted diet is a non-starter in a society where excess consumption has become – and continues to be, despite the Government's considerable efforts – the norm.

It may be cheering to discover from this mass of statistics that celebrities don't have as much influence as we'd all assumed. But if someone as successful and ubiquitous as Jamie Oliver can't persuade people to change their eating habits, I don't know what will.