Richard Black, head of mergers and collaborative working at the commission, told last week's open board meeting that some councils were undermining trustees' independence because they preferred to work with one organisation, not several.
"Having one funder can give the funding body a sense of ownership, perhaps because it knows that the charity has no other form of income," he said.
The board agreed to send councils commission guidance on the importance of diverse funding streams.
Dame Suzi Leather, chair of the commission, said she agreed with this action, but was in favour of similar charities choosing to merge.
John Williams, a member of the board, said: "It would be efficient to have one charity for the whole country, but it wouldn't be effective. We should let a thousand flowers bloom."