The NCVO has started a petition on the Number 10 website calling on the Government to reverse plans to charge charities and voluntary groups that play recorded music.
Charities have an exemption from paying fees to Phonographic Performance Limited, which represents music producers and performers, but this is due to be withdrawn in April after a consultation in 2008.
Charities and voluntary groups would have to pay fees for playing recorded music in, for example, charity shops or care homes. It has been estimated that this could cost the sector £20m a year.
The petition, which went up on the Number 10 website on Monday, calls on the Government to maintain the exemption for charities and voluntary groups.
"The Government's own figures suggest this change will cost voluntary and community organisations up to £20m more a year," it says. "This is an incredible amount of money, which can be met only by funds earmarked for charitable purposes."
The NCVO has written to business secretary Peter Mandelson asking for an urgent meeting to discuss the issue. Legislation to implement the change is expected to be put before Parliament in February.
A spokeswoman for the Intellectual Property Office said charities must be protected from excessive costs, but it needed to ensure that musicians and performers were fairly rewarded.
"PPL has agreed to operate some voluntary exemptions to its fees, meaning that some organisations will pay nothing," she said.
Fees for other organisations would be decided after consultation, said the spokeswoman, who urged affected organisations to make their views know to PPL and the Community Sector Law Monitoring Group, which examines legislation that will affect community organisations.