This is almost double the 14,787 out of 629,359 children (2.35%) of four and five year-old severely obese children in reception class.
The findings indicate that between starting and leaving school, average percentage rates of schoolchildren in the "severely obese" category, nearly doubles from 2.4% to 4.1%.
It follows figures revealed yesterday, which warned that 22,000 children were leaving primary school severely obese.
Severe obesity is measured in adults with a BMI of 40 or above, at least 60% higher than the upper healthy BMI limit of 24.9.
The LGA says action must be taken to prevent a generation of dangerously overweight children growing into a "multi-billion-pound ill-health time bomb".More news: Serena Williams Turns Things Around Against Ashleigh Barty
"This new report reflects some of our deepest concerns about childhood obesity".
MPs have called for a ban on the use of cartoon characters to advertise foods like McDonalds, KFC, and Burger King that are high in fat, sugar or salt.
The body "claims that £600m cuts to council public health grants is preventing work to combat childhood obesity" and urged the Government to reverse the cuts, the Times Educational Supplement reports.
Dr Modi Mwatsama, of the Obesity Health Alliance, said: "This is a superb report that reflects what obesity campaigners have always been saying - the United Kingdom is in the midst of an obesity epidemic and the Government must take strong measures to tackle childhood obesity if we're to prevent this spiralling beyond control".More news: Multivitamins and supplements don't provide health benefits
The Commons Health and Social Care Committee also wants more to be done to tackle obesity risks in the first 1,000 days of a child's life, including setting breastfeeding targets. Severe obesity can also shorten a person's life by 10 years - an equivalent loss to the effects of lifelong smoking.
Despite budget reductions, it said councils are spending more on running effective prevention schemes to help children stay healthy, which is key to tackling the child obesity crisis and reducing future costs to hospital, health and social care services.
MPs are also calling for a 9pm watershed on junk food advertising and says there needs to be a ban on brand generated characters or licensed TV and film characters being used to promote HFSS products on broadcast and other media.
Cllr Izzie Seccombe, chairman of the Local Government Association's community wellbeing board, said there is a clear need for everyone to take action.
"The UK is already the most obese nation in western Europe, with one in three 10 and 11-year-olds and one in five four and five-year-olds classed as overweight or obese, respectively".More news: Has Aaron Ramsey dropped a hint over his Arsenal future?
More children in Cumbria are starting school overweight than anywhere else in England.