The Directory of Social Change, which had supported the Government's position of leaving guidance on public benefit out of the Bill, has now changed its mind.
The NCVO has also changed its position, arguing for a requirement that the Charity Commission assess public benefit in the light of "modern conditions" to be written into the Bill.
The DSC said that the Charity Commission, which would interpret and police public benefit in the Bill's proposals, is taking a far too conservative approach.
The training and advocacy body claimed that the inability of some fee-charging hospitals and schools to show they benefit the public was a "running sore" for the charity sector.
And it said that the commission's latest guidance suggests that only schools and hospitals that "wholly" exclude people on low incomes will be at risk of losing their charitable status.
"Repeated papers from the commission, most recently last week, have taken the narrowest and most restrictive view possible of existing case law," said DSC researcher Luke FitzHerbert. "Given this, the public benefit proposals are likely to have a negligible effect."
The NCVO has redoubled its opposition to any statutory definition of public benefit. But it wants the Government to insert in the Bill a stipulation that the Charity Commission should give equal weight to "modern conditions" as to case law when assessing public benefit. This would mean consulting with the sector and the public at large.
"We see this as a solution to the Charity Commission's inability to change legal principles - they can't just go back and alter case law," said a spokesman. "But we don't want the other option of a statutory definition that is set in stone."
Liberal Democrat peer and charity lawyer Lord Phillips tabled an amendment to the Bill last week, with the support of the NCVO, to compel the Charity Commission to revise its public benefit requirements "in the light of changing laws or circumstances".
FitzHerbert said the DSC now supported the wording on public benefit criteria included in the Scottish Charities Bill last November. The wording stipulates that when deciding public benefit, sufficient regard must be given to whether benefit is to a section of the public only, whether conditions are unduly restrictive, and whether there is any disbenefit to the public compared to benefit gained.