One in 10 children was obese at the start primary school in England last year but one in five was obese by the end.
The reserach was carried out by to the Health and Social Care Information Centre.
Although figures for Reception children have fallen slightly, the figures for obesity in Year 6 are on the rise.
Children living in the most deprived areas were twice as likely to be obese as children in affluent areas.
Campaigners said the figures should act as a wake up call.
The figures for 2014-15 come from the government’s National Child Measurement Programme for England which covers all state primary schools.
By measuring children’s weight and height and calculating their BMI (body mass index) centile, they can be put into one of four categories: underweight, healthy weight, overweight or obese.
Among children aged four and five in Reception year, 9.1% were classified as obese – compared with 9.5% in 2013-14 and 9.9% in 2006-07, when records began.
In Year 6, 19.1% of children were obese – an increase on figures from eight years ago.
While one in four or five children was overweight or obese in Reception, one in three was either overweight or obese in Year 6.
The London boroughs of Southwark, Newham, Lambeth and Tower Hamlets topped the table for obesity among children aged 10 to 11 (Year 6).
The figures showed 28% of Year 6 pupils in Southwark were classed as obese and 44% were either obese or overweight.
Wolverhampton had the largest number of obese 10 and 11-year-olds outside London.
Waverley in Surrey reported the smallest number of obese pupils – 5% in Reception and 9% in Year 6.
Eustace De Sousa, national lead for children, young people and families at Public Health England, said tackling obesity was a major priority.
“While it is encouraging to see that overweight and obesity in children are levelling off, these figures are still unacceptably high and much worse in the poorest areas. The doubling of obesity levels between ages 4 and 11 is deeply concerning and highlights that much more needs to be done to help children and families.”
“We are committed to supporting local authorities by improving awareness locally, promoting the evidence behind ‘what works’ and providing advice to families through our Change4Life campaign.”