The organisation is establishing boards in England, Scotland, Wales and Northern Ireland that will decide how grants in each country are distributed.
Each committee will be responsible for managing, monitoring and setting strategy for programmes in its country. They will do so under the guidance of the fund's main board.
The fund is setting up the committees to comply with the 2006 National Lottery Act, which called for a more devolved framework of decision making.
Neil Cleeveley, director of information and policy at Navca, said the the umbrella group was happy for the fund to choose how it administered grants as long as there was transparency.
"I hope the England committee will stand up for the good causes and make sure we get more funding, and that money does not get subverted to the Olympics," he added.
Nick Aldridge, director of strategy and communications at Acevo, expressed concern that establishing four committees could increase the burden on organisations that spanned all four countries. Some fund grant programmes are UK-wide; others are for specific countries.
He described members of the chief executives body as being increasingly frustrated by applications that spanned national boundaries.
Aldridge said: "They are finding it increasingly difficult to coordinate work across boundaries. If they are now having to put in separate funding bids, that is going to increase the burden.
"We are all for national accountability and devolving decisions, but will want to make sure this is not just building structures."
The fund's board members with responsibility for covering each of the countries will chair the respective committees. Three members of the England committee are also members of the fund's main board.