Labour's education spokesman was angry after a parent at Silverdale comprehensive school complained about Mr Blunkett's reported comments that "vocal and well-placed parents" were trying to jump the queue for resources.
The parent, a Labour supporter, accused Mr Blunkett of hypocrisy and repeated claims that the council had discriminated against schools in the south-west of the city because it was relatively affluent.
Mr Blunkett replied: "I am not interested in class warfare either. I am not, however, keen on a headteacher effectively saying 'to hell with the rest of you - we are going to go for grant-maintained status, whatever it means for other schools and other pupils'. That, in my view, is a declaration of conflict, not my programme for the renewal and repair of all schools and a dramatic change in standards."
The school's head, Enid Fitz-george-Butler, a lifelong Labour supporter, says she was trying to protect her school. Last November she sent home 500 pupils after the top floor of the school's main building was declared unsafe and a classroom ceiling collapsed.
She said: "If Mr Blunkett thinks we are taking a selfish attitude because we considered opting out, presumably he would say the same about Tony Blair who sends his son to a grant-maintained school."
Sheffield says that Silverdale is not the only school in the city with severe problems. This year the Government allowed the council to spend only Pounds 260,000 on capital projects for all its schools.