Ofsted's incoming chair has become embroiled in a conflict of interest row after it emerged that she will continue to advise an academies chain despite her new role.
Sally Morgan, a former aide to Tony Blair, joins the board of the schools watchdog next month.
The TES has learned Baroness Morgan is to continue in her role as adviser to children's charity Ark, which runs a chain of 12 academies.
The 51-year-old has advised Ark's global board since she left Downing Street in 2005. She is also governor and chair of the curriculum committee at the Globe Academy in Brixton, London - one of the schools it runs.
NASUWT general secretary Chris Keates said: "Ofsted is an independent body in which the public must have confidence. The chair has to be able to comment without fear or favour.
"How can she do that when she's simultaneously advising the board of a body that has a vested interest in the expansion of academies?"
But Ark communications director Lesley Smith said Baroness Morgan's continued involvement in education would be beneficial in her new role.
"There's no reason whatever for her not to take (the position) up," Ms Smith said. "She is an adviser to the Ark global board.
"She will be part of the Ofsted board, which sets strategy and direction, and will have no influence on individual inspections.
"If Ark schools have issues with Ofsted, she will stand aside and let the deputy deal with it. The Department (for Education) was very clear on this point.
"All of the board have some involvement with educational bodies. (The Department) actively wanted people who do understand the system. They regard that as a positive thing."
But Anti Academies Alliance national secretary Alasdair Smith queried what would happen when Ofsted inspected Ark schools.
"If an Ark school is being inspected, an inspector should not be feeling some sort of conflict of interest.
"If a school was on the borderline of satisfactory and unsatisfactory, how would inspectors feel? It would be a vague area that I don't think is helpful. The chair of Ofsted has to be credible, and if she keeps her role as an adviser to Ark, I don't think she is."
Baroness Morgan is also an adviser to the New Schools Network, the organisation responsible for promoting the coalition Government's free schools policy.
Baroness Morgan, a former geography teacher, was Tony Blair's political secretary. She became a senior adviser when he entered Downing Street in 1997.
She has an MA from London University's Institute of Education, and also serves on its advisory committee.
A Department for Education spokesman said: "There is no conflict of interest between Baroness Morgan's roles.
"The separation of powers between the Ofsted board and the chief inspector ensures that neither the chairman nor individual members have any influence over specific inspection judgments."