Almost 70,000 premature deaths a year - more than one in 10 - could be avoided if people in the UK switched to a healthier diet, according to an analysis by the Cabinet Office.

A third of heart disease and a quarter of all cancers are thought to be diet-related. The critical issue for the coming years is to persuade us all not to eat more, but to eat better, the interim paper from the Cabinet Office strategy unit says.

The prognosis is worst for children, it warns. They eat a diet that is proportionately even worse than that of adults, and puts them at even higher risk of disease, disability and a truncated active lifespan, says the document.

Food-related ill health cost the NHS an estimated £6bn in 2002, which is 2% of its budget. Obesity, which increases the risk of a wide range of health problems, is projected to increase significantly.

"Obesity is one of the great challenges facing both the NHS and our society," said health minister Ivan Lewis. "While government alone cannot provide all the solutions, it is essential we offer strong leadership commensurate with the importance of the issue.

"That is why we will be using the analysis we are publishing today to inform the development of a radical long-term strategy to tackle obesity. This strategy, to be published later this month, will once again underline the centrality of prevention and public health at the heart of a modern NHS."

The largest number of premature deaths - 42,000 - could be avoided if people increased their fruit and vegetable intake by 136g a day.

Most people and most children are still not eating five portions of fruit and vegetables a day, although the numbers have risen - the Health Survey for England found that by 2005, 26% of men and 30% of women were eating five portions a day, almost double the numbers in 2001.

A further 20,000 premature deaths could be avoided if we reduced our average daily salt intake from 9g to 6g. Most of our salt - 75% - comes, without some people realising it, from processed foods. Men consume almost double the amount of salt that they should, increasing the risk of high blood pressure and stroke.

Cutting saturated fat, typically found in pies, crisps and cakes, by 2.5% of our total energy intake would prevent a further 3,500 deaths, the paper says. Too much saturated fat raises the risk of heart disease and cancer as well as contributing to diabetes and obesity. Cutting back on added sugar (as opposed to natural sugars for instance in fruit) by 1.75% of our total energy intake would prevent a further 3,500 deaths.

Consumption of oily fish is still well below the 140g a week recommended, especially among younger people. Only 3% of children and 15% of adults from low income backgrounds eat it.

Children's diets look much like adult diets, only worse. The largest single source of sugar is in soft drinks such as colas (not fruit juice); they eat only 2.5 portions of fruit and vegetables a day and far too much saturated fat.

The report notes that lifestyles have changed. People want convenience in their shopping, cooking and eating out but they are increasingly interested in where their food comes from and how it is produced.

They say they want to eat more healthily, but "there is a gap between what people do and what they say". This also shows in their aspiration to cook real food and control their children's eating habits, which may not become reality.