"There could be conflicts of interest and it could compromise the role of the chief executive as head of the paid service," says Tory group leader Margaret Eaton.
School governors are, after all, responsible for large amounts of council money. Governing bodies have big responsibilities overseeing the school. They may be under pressure to cut budgets or make staff redundant. Or they may want to go to outside contractors instead of buying into the council's in-house services. Would it therefore be more difficult for a governor to act in the best interests of the school if they are going home to someone working at policy-maki ng level on behalf of the authority?
Mrs Penn robustly defends her position. She has, she points out, been a magistrate and a member of Bradford health authority, and is perfectly capable of forming her own judgments. She regards the objections as sexist.
"In any situation you have to do what you think is right. My priority as a governor is to do the best for the school. I'm very clear about my husband's role. I can't imagine a situation where his view would affect what I might do as a governor. We generally don't even discuss these things. I can't see any conflict of interest."
There is nothing in the law to prevent such an appointment (Cherie Booth, wife of Prime Minister Tony Blair, is a governor at a primary school in Islington, north London), though the regulations might require Mrs Penn to withdraw when certain matters involving the council are under discussion.
Mr and Mrs Penn are, no doubt, able to exercise their judgments independently. But, as the Labour Government has found over the question of donations to party funds, appearances may matter, too. People will talk,and what they think, however unjustified, may be damaging to the council's reputation.
Ian Rule, secretary of the National Association of Governors and Managers, believes that, on the face of it, appointments like that of Mrs Penn are unwise. "As in so many things, it comes down to the people involved," he says. "There are lots of grey areas involving questions of judgment, and there will always be people ready to snipe."