The £3.55bn investment scheme promises to rebuild or refurbish half of all primary schools within the next 15 years.
Knight said nine out of 10 local authorities are prepared to receive their share of funding for the Primary Capital Programme.
But 15 local authorities have struggled to prepare for the scheme and need support from the Department for Children, Schools and Families to strengthen their plans.
Knight said: "We want every area to benefit from this sustained investment and fully expect every local authority to have a robust, approved plan in place shortly".
Children's Secretary Ed Balls explained that investment in public services is "vital" despite the credit crunch.
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