Twelve charitable purposes are included in the bill, including a category covering the "advancement of citizenship" not previously spelled out in government plans.
But the definition of public benefit remains undefined, leaving the Charity Commission to interpret charities' compliance on the basis of historic case law.
Charities Minister Fiona Mactaggart attempted to assuage the fears of public schools that they could be removed from the charities' register by asserting that "everything that is charitable now will continue to be charitable when the law comes in".
The commission will undertake a "scoping exercise", primarily with fee-charging schools, to ascertain whether they pass a public benefit test.
Factors determining their success will include whether fees are so high that they exclude the less well-off, and whether those who can't pay get help to access services. The commission's guidance, The Public Character of Charities, is currently being revised.
But Andrew Phillips, a Liberal Democrat peer and a member of the parliamentary committee that will scrutinise the draft bill, said some attempt to define public benefit in the Bill might be needed.
"My main interest in cross-examining witnesses and hearing evidence will be to decide whether the Bill should contain some guidance criteria by which public interest can be judged," he said. "I'm certainly not in favour of exhaustive definition, but a guidance statement might be helpful."
The draft bill reaffirms the promotion of human rights as a charitable purpose, but it is not clear if it will resolve the legal complications of the current definition.
At the moment, organisations such as Amnesty can campaign through their charitable arms in countries that enshrine human rights in law, such as the UK, but not in countries that don't.
However, Mactaggart indicated that the Bill would simplify matters.
"I'm confident that the overwhelming majority of what Amnesty does, not only in the UK, will be charitable," she said.
A spokeswoman for the NCVO expressed concern that the Bill did not include provision for rolling public character tests for charities, to be undertaken by the Charity Commission: "It's not explicit in the Bill. We want a clear indication of what the commission's role will be," she said.
The NCVO also noted an expansion of the commission's powers in the Bill in the form of a regulatory objective to "encourage charities to maximise their social and economic impact". "Legally, charities don't have to do that. We will be using the scrutiny process to find out exactly what that means," said the spokeswoman.
Luke FitzHerbert, researcher with the Directory of Social Change, warned that the Bill gave the Charity Commission unprecedented power to "effectively act as the court of decision to decide charitable status on a case-by-case basis".