John Grogan, the MP for Selby, has put down an amendment with other Labour and Lib Dem MPs saying that the Charity Commission, when it assesses whether a charity provides public benefit, should consider "the effect of placing any undue restriction on obtaining that benefit".
The amendment, which is to be considered at the report stage of the Bill today, and is supported by a group of about 40 Labour and Lib Dem MPs, was also backed by the NCVO until recently.
Grogan said he had received about 20 calls from voluntary organisations protesting about the NCVO's acceptance last week of the Government's refusal to concede the amendment. "I don't think I've ever seen the chief executive of a major organisation do a U-turn so fast and for so little," Grogan added. "It was very weak negotiating."
The NCVO's support of the amendment was seen as crucial in the drive to get ministers to change their minds, but it is unclear to what extent it has influenced the voting intentions of MPs.
Grogan said: "Ultimately, there is the parliamentary arithmetic: the Conservatives will support Ed Miliband, so he has a majority whatever happens on the Labour and Liberal Democrat backbenches."
Stuart Etherington, chief executive of the NCVO, said that the amendment would have been preferable, but it had become clear that ministers were not prepared to concede it because of their fear of "unintended consequences".
It was felt that an organisation providing public benefit - a religious organisation, for example - might not be able to demonstrate it if the amendment was passed.
Etherington said ministers had conceded instead that the planned review of the legislation would take place after three years rather than five, and the commission had been developing "a robust position" on how it would implement the public benefit test (see story above).
This meant, he said, that if the Government's desire for a robust public benefit regime, made explicit in Parliament, was not working in practice - perhaps because of a challenge in the courts - it could hold an earlier review.
"This in turn will give the commission confidence to push the envelope as it develops the test of public benefit," said Etherington. "I reckon that amounts to belt and braces. We did say we would back John's amendment.
We also said that, if there was movement by the Government, we might not continue to support it.
"In our judgement, there has been movement, and the Government has gone as far as it can."