The National Audit Office study shows that poorer children are twice at risk of obesity than well-off kids. Black youngsters are also more prone to being very overweight than white counterparts. The Whitehall spending watchdog accuses successive governments of struggling to tackle the ticking time bomb.
The 60-page study warns: "It is not clear that the Department of Health and Social Care's current programme will be able to make the step change needed in the timescale available."
In 2018/19, 9.7 percent of four to five-year-olds and 20.2 percent of 10 to 11-year-olds in England were obese, it says.
Children in deprived areas were twice as likely to be obese compared with those in less deprived communities.
Nearly 13 percent of four to five-year-olds were obese in the most hard-up areas compared with 6.4 percent in the least deprived.
The gulf widened at ages 10 to 11, with 26.9 percent in the most deprived areas classified as obese against 13 percent in the least deprived.
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The NAO study also lays bare the costs to taxpayers, citing a government estimate that obesity cost the NHS £6.1billion a year - soaring to £27billion when the cost to wider society was taken into account.
NAO chief Gareth Davies said: "Tackling childhood obesity is a major challenge, and one that governments have struggled with since the 2000s.
"It is clear that children living in deprived areas or from ethnic minorities are far more likely to be obese - and the problem is worsening.
"Progress with the Childhood Obesity Programme has been slow and many commitments are not yet in place.
"The new strategy announced in July has signalled a greater intention to tackle obesity but the Government will need to follow through with more urgency, commitment and cohesion if it is to address this severe risk to people's health."
Ian Hudspeth, Chairman of the Local Government Association's Community Wellbeing Board, said: "Childhood obesity is one of the biggest public health challenges we face and this report is another stark reminder of the urgent need for radical action to combat this."