Public benefit issue dominated the debate at the committee stage.
A five-strong group of Labour and Liberal Democrat MPs is supporting a new amendment on public benefit for consideration at the report stage of the Charities Bill in the autumn.
The move follows completion of the Commons committee stage, when earlier amendments on the subject from the Liberal Democrats and the Conservatives were rejected by the Government.
The fresh amendment, put forward by Labour MP John Grogan, says: "In determining whether a body provides public benefit, regard must be had to any undue obstacle in obtaining that benefit."
It is the latest attempt to deal with concerns about whether fee-charging charities, such as independent schools and hospitals, give enough back to the community to justify the tax advantages of charitable status.
The amendment is supported by the NCVO as well as by MPs. Stuart Etherington, chief executive at the NCVO, said: "We hope the Government accepts this amendment or comes forward with its own amendment, agreed with the Charity Commission. This would ensure that the Bill really does put public benefit at the heart of charity law."
The question of fee-charging charities and public benefit took centre stage in the eight sittings of the Bill's committee stage, completed in 10 days earlier this month.
Efforts by Martin Horwood, the Liberal Democrat spokesman on the Bill, to introduce the same wording that is used to judge a charity's public benefit under Scottish law, were easily defeated by the Government.
The Conservatives joined Ed Miliband, minister for the third sector, and colleagues in voting down the amendment, which would have denied charitable status to bodies with "unduly restrictive" fees, by 12-2.
Miliband said the Government has not closed its mind to improving the Bill in regard to public benefit, but the wording of the Scottish amendment was not clear enough and could have unintended consequences.
He said: "Could we be sure, in the context of the law in England and Wales, that existing charities that charge fees, such as museums, would not be caught?
"At best, it would mean no change to the public benefit test that is carried out by the commission. At worst, it could have harmful effects."
Shadow charities minister Andrew Turner was forced to withdraw amendments designed to reinstate the presumption that has existed in charity law since 1601, that educational, religious and poverty-relieving charities work for the public benefit. The Charities Bill removes this presumption on the grounds that all corganisations claiming charitable status and the accompanying tax breaks should demonstrate public benefit.
The Government did show flexibility in other areas of the Bill, however.
Miliband has pledged to investigate how and to whom the Charity Commission could be made accountable in Parliament, after both the Conservatives and the Liberal Democrats made the case for parliamentary scrutiny of the commission's activities.
Although the Bill will allow for charities to appeal against commission decisions through a new charity appeal tribunal, both parties made the case for a further mechanism through which the commission can be brought before Parliament.
"I hear what the committee says," responded Miliband. "I shall continue discussions with other members, and I hope to report progress."