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County education chiefs say they will need to find an extra 15,000 primary school places over the next five years - 5,000 more than they had forecast.
The startling 50% increase has been blamed on more people coming to live in the county, an increase in the birth rate and the upturn in the economy leading to more homes being built.
Kent County Council said it was responding to the increase by making plans for schools to expand and for new ones to open.
Opposition councillors say KCC has taken its eye off the ball and should have foreseen the surge in demand.
KCC says the impact is county-wide but some areas are under particular pressure, including Gravesham, Swale and Sheppey.
Cllr Roger Gough, the Conservative politician in charge of Kent schools, said the authority was taking steps to create more places but acknowledged earlier forecasts had under-estimated the scale of demand.
He said accurate forecasts were “extraordinarily difficult to get right.”
“There is no doubt the overall number we predicted has been a bit greater than we forecast. We are seeing very localised pressure in Gravesham, Tunbridge Wells and Sheppey.
"We are having a large expansion of places this year, including an extra 29 forms of entry [new classes] and seven new primary schools.”
The county council’s education director Patrick Leeson said inward migration into the county was “a very significant factor” and there was a detailed two-year plan to address the shortfall.
But he warned long-term forecasting was difficult and no-one could judge the scale of demand in the years ahead.
Cllr Gordon Cowan, Labour spokesman, said: “We are fighting a losing battle on this.”
The pressure for more places is set out in the latest version of KCC’s plan to respond to changes in numbers.
It states: “The number of primary-aged pupils is expected to continue rising significantly from 114,275 in 2013-14, to 129,338 in 2018-19, which is more than 15,000 extra pupils over the next five years.”
Next year, KCC will need about 30 new forms of entry, most of which will be needed for 195 reception-aged pupils.
By 2018, it expects to have added a total of 111 extra forms of entry.
The commissioning plan says the number of reception age pupils in Kent schools rose from 14,812 in 2007-08 to 17,273 in 2013-14, a 17% increase.