Labour and the Liberal Democrats have welcomed his decision for "a broad-brush review" of grant-maintained schools, further education colleges, universities and training and enterprise councils. But they fear that it will not go far enough.
The governing bodies are neither fully elected nor appointed by ministers and are, therefore, not affected by the rules on quangos proposed by the Nolan committee on standards in public life. But they are largely publicly funded and the committee has powers for more detailed investigations.
Don Foster, the Lib Dem education spokesman, said his demands for information from ministers on the accountability of GM schools, the Office for Standards in Education and FE colleges have been met with nothing but buck-passing.
He said: "When I asked for information on OFSTED, the Minister said, 'It's nothing to do with me' and referred me to the chief executive Chris Woodhead. " Efforts to have education minister Tim Boswell intervene in a recent dispute at Bath College of FE were met with a similar response, he said.
"I was referred to the Further Education Funding Council, who referred me to the governors, and the governors said they had delegated responsibility to the principal - a key protagonist in the dispute."
The Nolan committee has said it will look not only at how officers and staff are appointed but at the safeguards against potential conflicts of interest. The Labour party insists conflicts can be minimised by extending public accountability.
Charles Bell, of the education pressure group Article 26, said: "Lord Nolan should look at the grievance procedures in FE colleges, GM schools and TECs. All the real criticisms are coming from the whistle-blowers, not the FEFC. "
With the loss of local education authority control, a safety valve which let an aggrieved person appeal to an inspector or a higher court had gone.
"Now there's no way out from a management decision other than an industrial tribunal or the law courts," he said.