A report published by the think-tank The Food Foundation calculated the bottom 20 per cent of families would have to spend 42 per cent of their income, after housing costs, on food in order to eat the government's recommended diet set out in the Eatwell Guide.
Published by Public Health England (PHE), the guide suggests a balanced diet would cost £41.93 a week for an adult.
The Food Foundation used this data to estimate that a family of four - two adults and two children aged 10 and 15 - would need to spend £103.17 a week to follow the Eatwell Guide - a total of £5,364 a year. The poorest 20 per cent of families, containing 3.7 million children, have household incomes of less than £15,860 a year.
The richest 50 per cent of households need to spend just over a 10th (12 per cent) of disposable income after housing costs to eat a healthy diet.
The foundation said the unaffordability of a healthy diet for low-income households is highlighted by higher rates of childhood obesity in deprived areas of the country, with more than a quarter (26 per cent) of year 6 children in the most deprived areas of England being obese, contrasted with obesity affecting just 11 per cent of children of the same age in England's richest communities.
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Food Foundation executive director Anna Taylor said the government needed to take cross-party action to make it possible for families to eat healthily, as a result of the findings.
"The government's measurement of household income highlights the fact that millions of families in the UK cannot afford to eat in line with the government's own dietary guidance," she said.
"It's crucial that a co-ordinated cross-government effort develops policy that accounts for the cost of its recommended diet, and creates a food system that does not consign those on lower incomes to the risk of diet-related illness."
The report recommends that the government addresses the problem by strengthening programmes that support better nutrition, such as the Healthy Start vouchers that provide fruits, vegetables and milk to low-income children, and free school meals.
But PHE chief nutritionist Alison Tedstone said factors other than income were to blame for poor diet.
"Our food choices are affected by other factors such as the volume of fast food outlets on our streets and promotions of unhealthy foods in our shops, highlighting why our work to improve the nation's diet is so important," she said.
"This report suggests a healthy balanced diet in line with the Eatwell Guide costs around six pounds per day for an adult - we are currently spending about the same amount eating poorly."
In May a health and social care select committee report called for urgent action to prevent childhood obesity, including greater regulations around discounted price offers on unhealthy foods, and the introduction of a 9pm watershed for "junk food" advertising.