They fear that the proposal, which could be implemented in 2006, may reduce charity funding or make organisations more dependent on the Government.
A collaboration of London agencies headed by the Greater London Enterprise, the London Voluntary Sector Training Consortium and the Mayor of London have united in opposition to the move. Umbrella groups in Scotland, Wales and Northern Ireland are also have reservations.
"At the moment the EU keeps the Government on the straight and narrow," said John Goodman, a member of the Third Sector European Network, which helps voluntary organisations with structural funding. "If the EU hands responsibility for the funding to the Government, there is a danger that the money might be used to fund public services."
The UK will have received £10 billion through the seven-year structural funding scheme when it expires in 2006. The money is not exclusively for charities but is allocated to not-for-profit projects.
Competition for funding will increase dramatically when the EU expands from 15 to 25 members in 2004, because the new states are less well off than existing members. To combat the problem, the EU has launched a review and asked members to submit proposals for a new system to replace the existing structure when it finishes in 2006.
There are three strands of EU funding - objective one, two and three - to support the social and economic restructuring of deprived areas across the union.
The UK Government's proposal includes ploughing all objective one funding into the new member states and repatriating objective two and three funding so that it is distributed by domestic governments rather than by the EU.
It claims this will save money on bureaucracy, a claim which is disputed by Will Roberts, spokesman for the Greater London Enterprise. He said: "There is little evidence that the UK Government is less bureaucratic than the EU, and it may even be worse."
Groups are also worried that repatriating the funding will sever links between member states created to share best practice and experiences.
"It begins to isolate the UK from Europe and the various networks that the regions have developed could be lost," said Phil Fiander, director of Europe at the Wales Council for Voluntary Action.