Last week, the Charity Commission said it was unable to "clarify" whether it had the power to withdraw charitable status from already registered charities that failed a public-benefit test.
But the Charities Bill Coalition, comprising more than 20 charities including Cancer Research UK, Amnesty International UK and the NSPCC, said that without an enforceable public-benefit test, it will not support the Bill.
Last week, in private evidence to the Parliamentary scrutiny committee, the Charity Commission claimed that it could not retrospectively overrule "exceptions to general public-benefit principles".
The commission said that while it could carry out public-character tests on all existing charities, including public schools, it had yet to clarify what action it could take if they did not pass.
But a spokesman for the coalition said: "An enforceable public-benefit test that can be used by the regulator on existing charities to require them to meet certain criteria, has to be there.
"If the scrutiny committee isn't able to get that in, we will be tabling an amendment when the Bill comes before Parliament."
The Home Office questioned the commission's stance. "Our position is that when an organisation is no longer for the public benefit it ceases to be a charity and it must be removed from the register."
A commission spokeswoman that said that in cases where charities did not show public benefit, it would work with them to help them improve.
In extreme cases, it would consider other action such as redirecting charitable assets to purposes close to the original aim.