Among reception-aged children – those aged four and five – the rates of obesity rose from 9.9 per cent in 2019/20 to 14.4 per cent in 2020/21.
For those aged 10 and 11, who are in their last year of primary school, obesity prevalence increased from 21 per cent to 25.5 per cent.
It means that overall, 27.7 per cent of pupils were overweight or obese by the age of five, compared with 23 per cent the year before.
Two fifths of children have weight problem by age 11
And by the age of 11, 41 per cent of children have a weight problem, the statistics show.
The statistics also show far higher rates of obesity among boys compared with girls by year six, with 29.2 per cent of boys obese compared to 21.7 per cent of girls.
The scheme normally weighs and measures children throughout the school year.
But with schools closed for much of the pandemic, officials were only able to restart the programme in March 2021, a year after lockdown.
Officials said that the volume of data for 2020/21 was more limited than that for 2019/20, as a result.
On Tuesday health officials announced that 1,000 children a year will be offered diet plans, mental health and coaching.
The specialist help will be aimed at those suffering health complications related to severe obesity.
Health officials said families would be offered “group sessions” including support from dietitians, psychologists, specialist nurses, social workers, youth workers and paediatricians.
Amanda Pritchard, the chief executive of the NHS in England, said: “The pandemic has shone a harsh light on obesity – with many vulnerable young people struggling with weight gain during the pandemic.
“Left unchecked, obesity can have other very serious consequences, ranging from diabetes to cancer.
“This early intervention scheme aims to prevent children and young people enduring a lifetime of ill-health.”