The would-be deputy Labour leader wants private schools to do more to justify their tax breaks. "It's not enough just to lend their playing fields; it's about opening up their science labs, lending their teachers to the state sector, sponsoring academies and forming trusts," he said.
The pronouncement irked state school staff. "Private schools have a massive amount to learn from state schools," sniffed a National Union of Teachers'
Meanwhile, independent sector heads accused Mr Johnson of playing at "the politics of envy".
And Eton is refusing to play ball. Tony Little, its headmaster, has said that he wants nothing to do with the academies scheme, touted as one way for private schools to retain their charitable status.
"We won't be foolhardy enough to claim the wherewithal to run a school in the inner city," he said, with refreshing modesty.
Still, where Eton fears to tread, Ginsters is only too happy to go. David Samworth, the businessman behind the celebrated pasties, has pledged to sponsor a new academy in Nottinghamshire.
The Daily Mail reports that even the Department for Education and Skills cannot take Labour policy seriously, after discovering a page on its website proposing trust schools named "blah blah", "rubbish" and "up yer kilt", with supporting partners such as "Heinz soup", "Rolf Harris" and "Majorca".
A spokesman said, with an admirably straight face: "The site is not yet operational. As with any public resource, it has been tested in advance using fictional data."
The grammar schools controversy limps on, with Conservative frontbencher Graham Brady resigning after claiming that selective schools boost the results of an entire neighbourhood. David Cameron, the party leader, angered core voters when they noticed, belatedly, that he had spent the past 18 months saying he would not expand selection if the Tories gained power.
The party's new big idea is to allow inner-city schools to select children by race to ensure a good ethnic mix. David Willetts, shadow education secretary, said it wanted to tackle "the growing ethnic segregation in our schools".
And psychologists have been on the offensive. Dyslexic children have been dismissed as "lazy, thick or stupid" by Julian Elliott, an educational psychologist who has accused middle-class parents of using the diagnosis as a fig leaf for their children's inadequacies.
Another psychologist criticised pushy parents for buying Ritalin, the hyperactivity drug, to pep up their children's exam performance.