The Charity Commission will check on whether or not private schools pass the test of "public benefit", in light of the new Charities Bill. All independent schools will have to prove they are worthy of tax breaks when it becomes law.
This week the Socialist Educational Association called for the five-member board which heads the Charity Commission to be replaced. It followed an inquiry under the Freedom of Information Act which revealed that all the non-executive commissioners, appointed by the Home Secretary, attended independent schools. Tony Mitchell, vice-chair of the SEA, said that the admission cast doubt on their "ability to be impartial".
Two of the five board members also had husbands or wives who attended private schools and four had children at such schools.
Geraldine Peacock, the chairman, attended a direct-grant school and her three children were sent to private secondary schools.
The claims have been outlined in a letter to Fiona McTaggart, the charities minister.
Mr Mitchell said: "With the best will in the world, and I am sure that they are all honourable people, they cannot be truly impartial in this particular role and should not have it imposed on them. Not only must justice be done, it must be seen to be done.
"Someone else must be appointed to do this job."
The Bill, the first major reform of charity law in 400 years, is in the House of Lords, and is expected to become law before the general election.
A spokesman for the Independent Schools Council said it was "nothing short of offensive" to claim those who went to private schools would be biased.
He said: "The Charity Commission will have to consult widely on the public benefit test, almost guaranteeing transparency and impartiality."
A spokesman for the Charity Commission said all board members were impartial, adding: "We responded to Mr Mitchell's request in the spirit of openness, not because of any compulsion: the information was not held by the commission and some effort was required to assemble it." The board represented a wide range of experience and expertise, he said.