The shortage of primary places in the South East is now critical, local authorities struggling to meet demand for reception provision have warned.
A call for more funds has been led by Clive Webster, director of children's services at Southampton County Council.
Writing to the Government on behalf of 19 local authorities in the region, Mr Webster said: "The South East region of England is facing its most severe shortage of primary school places. There is a statutory duty that requires that this shortfall is met - and met in ways upon which parents can rely.
"The region's predicament is now critical. Additional and substantial government funding is essential so that this most basic of statutory duties - a primary school place for all who want one - can be met."
All 19 local authorities in the region are forecasting an increase in the number of primary-aged children in the coming years. One- third say they will not have enough places by September 2014, which is predicted to be the crunch year when the region will be short of about 750 places, assuming there is no added provision.
Some funding for additional places was given to three authorities in the region by the previous government.
But Mr Webster has challenged the Department for Education's calculations, saying that Southampton missed out on extra cash.