And this extension of parental power will not be confined to failing schools. A Labour source told the Sunday Times that "the new power is not meant for basket cases but schools which are muddling along".
As a parent, the promise of power to sack headteachers and governors worries me. We may know that Mrs X, who teaches history, is somewhat shaky on Roman Britain or that Mr Y has difficulty preventing young Darren from smashing test-tubes in the science lab, but that's a bit different from deciding that the place needs new management.
Are parents really the best people to decide that a school isn't up to scratch?
In 1997, a middle-class primary school in Cambridge, which appeared to be "muddling along" just fine, failed its Ofsted inspection. While some parents were relieved, many were amazed and outraged. Indignant letters from dons, doctors and journalists poured into newspaper offices. A few years earlier, one of the most over-subscribed church primaries in London was also found to be failing its pupils.
The latest Labour wheeze, in fact originally a Tory idea, overlooks two things. The first is that most parents think their children are at a reasonable school - only 4 per cent of them are dissatisfied, according to the most recent FDS International survey in The TES.
The second point is that parents want different things. The dons who defended the Cambridge primary school would shock Labour's literacy and numeracy zealots. They said they weren't worried that their children weren't learning to read at the speed judged appropriate by inspectors.
They didn't want pupils put under pressure. And they liked the multi-culturalism, French and judo that the school offered.
So the new power would divide parent from parent as one group called in inspectors to overturn a management team which another group backed. It would also divide parents from teachers.
What will happen if Ofsted decides that the complaining parents are wrong? The school's head and governors will have to carry on working with them.
Even the threat of parental revolt will put at risk those good relationships with parents so carefully nurtured by teachers.
Ministers, backed by overwhelming research evidence, have preached endlessly about the need to involve parents. Then, just as those partnerships are beginning to take root, they have come up with a scheme which could pull them apart.
But it won't - because parents have far too much sense to let it happen.
The parents who last week announced that they had government backing to set up a new school in Lambeth are exceptional, and prompted by desperation - the London borough needs thousands more school places. And they did not have to kick out a head to make it happen.
Politicians have always misunderstood the sort of power parents want. They want schools to listen when they have a problem with a teacher, or when their child is bullied. They want frequent reports on their child's progress and advice on how they can help. But most of them think running schools and sacking headteachers should be left to the experts.