Private schools and hospitals in England and Wales should lose their charitable status, a powerful committee of MPs and peers has said.
Private schools say they can show they benefit the public
The joint committee on the Draft Charities Bill said they might still get tax breaks if they could meet a "public benefit" test.
This goes beyond the government proposal that they should lose the automatic right to be charities.
Instead the Charity Commission would decide which organisations to register.
But the MPs and peers want ministers to go further.
Their report, just published, said "we believe that the government should consider reviewing the charitable status of independent schools and hospitals with a view to considering whether the best long term solution might lie in those organisations ceasing to be charities but receiving favourable tax treatment in exchange for clear demonstration of quantified public benefits."
The committee was chaired by Labour MP Alan Milburn prior to his return to the Cabinet earlier this month.
During one committee hearing he said opinion surveys indicated people were "amazed", even "aghast" or "appalled", that independent schools and independent hospitals enjoyed the tax perks of charitable status.
In response to the committee's report, the Charities Minister, Fiona Mactaggart, said: "I am very confident that we are on the right track to produce legislation that will benefit charities, will enable them to play an even bigger role as a force for good in society, and will encourage people to give their time, talents and money to charities.
"We will now be studying the committee's recommendations in detail and will respond to them in due course."
At present about 80% of independent schools are listed as charities, gaining tax benefits.
In a statement, the Independent Schools Council said there was overwhelming evidence of the public benefit provided by its member schools.
They educated half a million pupils at virtually no cost to the public purse, saving the country £2bn a year - more than 20 times the amount of the tax breaks they received.
"Those children are of all abilities and come from a wide variety of backgrounds; nearly a third of them receive help with fees."
Schools were committed to working "as part of the nation's education system" and increasing their partnership with state schools and the wider community.
The council looked forward to working with the Charity Commission on the standards for assessing public benefit.
It pointed out that the committee's most radical suggestion, about the loss of charitable status, was not actually one of its recommendations.
The Charity Commission has said the test it will set an organisation wanting to register as a charity will be whether or not it can show it is "delivering benefit to the public, or a sufficient section of it".
In addition, it must have purposes which are "exclusively charitable".
After the bill becomes law, the commission says it will need to ensure that every organisation on its register "actively shows that it is set up for public benefit".
The joint committee said it welcomed the government's proposals for reform and modernisation of charity law, which was "long overdue".
It was particularly keen to ensure that smaller charities were not "over-burdened by regulation", and it wanted charities to have greater freedom to trade.
The committee's report, which was unanimous, has 52 recommendations in all.
These include an additional charitable purpose, for "the provision of religious harmony, racial harmony, and equality and diversity".
The draft bill defines 12 charitable purposes, the existing three: the prevention or relief of poverty, the advancement of education and the advancement of religion.
And it has eight new ones, already recognised in case law, for the advancement of health, citizenship or community development, the arts, heritage or science, amateur sport, human rights, conflict resolution or reconciliation, environmental protection or improvement, animal welfare, and for the relief of those in need, by reason of youth, age, ill-health, disability, financial hardship or other disadvantage.