The chief executives body acted after it emerged that the lottery distributor is giving £45m to support last week's Government plan, prompted by TV chef Jamie Oliver, to improve the UK's school meals.
Acevo chief executive Stephen Bubb condemned the funding of the new School Food Trust as "completely improper use of lottery money".
He has written to the fund asking it to make public its communications with the Department for Education and Skills.
A spokeswoman for the Big Lottery Fund denied that the distributor was funding the food trust at all. "We have agreed in principle to give it £45m, but we will not release any money unless there are good plans consistent with our objectives," she said.
Nonetheless, charity sector representatives criticised the fund for using lottery funds to support a government initiative. Lindsay Boswell, director of the Institute of Fundraising, said the move was a "disgrace" that would result in charities losing millions of pounds.
The NCVO said it was "another example of the Big Lottery Fund misinterpreting the additionality principle". But Peter Melchett, policy director of the Soil Association, said that was unfair.
"The lottery has been actively interested in supporting work to improve school meals for at least three years, and has had detailed discussions with the Soil Association about how it can help over the past 18 months," he said. "It was always important that the lottery waited for new government policy."