Data drawn from the National Child Measurement Programme also showed nearly one in three children in year 6 (aged 10- to 11-years-old) are overweight.
The programme, which is overseen by the Department of Health, used body mass index to calculate the weight of nearly one million children in England.
Tim Straughan, chief executive of the NHS Information Centre, said: "Obesity is one of the biggest threats to health of our nation and it is of huge concern that the problem is afflicting so many children and at such an early age."
This year 88 per cent of eligible children were weighed, compared to 80 per cent last year. But there has been little or no change in levels of childhood obesity since 2007, the NHS report said.
The National Obesity Forum's clinical director, Dr David Haslam, said this was an alarming sign of Britain's failure to get to grips with the problem: "It's too late now to talk about prevention. Our children are facing a ticking time bomb of diabetes and heart disease."
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