Sources of Strength, from the Baring Foundation, says the threat comes when core services are disrupted by the "mechanics of contracting".
"Charities don't think about their independence until they are threatened from outside," said report author Cathy Pharoah, director of research consultancy Third Sector Prospect. "What often jolts them is a threat to the budget."
The report is based on a survey of applicants for Baring Foundation grants aimed at strengthening charities' independence from government.
Those charities that responded cited budget cuts due to policy changes, including changes of government funding priorities, as the main threat.
There was also widespread concern over contracts, particularly the problem of securing full cost recovery. "Voluntary organisations feel most under threat when their core services are jeopardised by the mechanics of contracting," the report says. "Voluntary organisations are not opposed to change per se; their problems is they feel unable to influence change when they feel their clients have a lot to lose from it."
However, organisations believe they can take practical steps to strengthen their independence once they are aware of the problem.