While more funds are flowing into education, much of the money has been ringfenced for projects - such as homework clubs or reducing infant class sizes.
This reduces schools' discretion to put money where they think it can be best used to raise standards - especially when core, pupil-related funding, is not increasing, said Pat Petch, chairwoman of the National Governors' Council.
She is calling for a national debate on how schools are funded.
"The trouble is schools were expecting money this year, and a lot haven't got it," she said.
"The additional funding is coming in little parcels for particular initiatives. You can open after-school clubs for this or that, but you haven't got the money to keep the core business of the school going."
Her own school is receiving a welcome pound;2,000 for new books -but believes the money would lead to a bigger improvement in standards if the school were free to spend the cash on additional classroom assistant support for pupils instead.
The Government has said it will review how it distributes education money to local councils via the standard spending assessment system. But ministers have imposed a three-year freeze on any further changes.
"They have got to do something much faster," said Mrs Petch. "The reason we won't be hitting the targets is we can't put in place everything we know we need to put in place to hit them.
"We need an open debate about how schools should be funded. It's schools that are going to move those children along and have to hit the targets."