One of the most memorable lines in David Cameron’s speech to the Conservative conference yesterday was this peculiar boast: “I’m not here to defend privilege, I’m here to spread it.”

It was an arresting assertion that didn’t seem quite to say what it wanted to. Privilege can only be usefully defined in reference to those denied access to it. A measure of exclusion is integral to the concept, so it cannot be universal. I don’t think the Prime Minister intended to say that he planned to hoist a few more people into the ranks of an impenetrable elite.

What he was trying to say, judging by the context, was that he would like everyone to enjoy an education of the standard that is today considered a rare privilege. A less memorable line that makes sense of the argument came a little earlier in an extended passage on Academies and Free Schools. Cameron described his plan for “millions of children sent to independent schools - independent schools, in the state sector.”

It is worth reading the education section of the speech in full (the text is here) because it contains an argument that is central to the Conservatives’ next election campaign and deeply challenging to Labour.

When you strip out some of the gratuitous union-bashing and snide digs at a 1970s caricature of the left-leaning educational establishment, you are left with an important political calculation. It is that parents are attracted to the idea of Academies and Free Schools because they think they will equip children with the kind of education, skills and confidence that private schooling has traditionally offered, only free of charge. This proposition is central to the Conservative pitch to “aspirational voters”. It assumes that the reason a small minority of people educate their kids privately is because they want to purchase a head start in life for their offspring. It assumes also that many of the rest would gladly acquire the same service but don’t because they can’t afford it. In broad political terms, those seem like pretty sound assumptions.

There are of course people who could pay school fees but choose not to educate their children privately. Some have access to brilliant state schools (often having paid the equivalent of school fees in a house price premium for the desirable catchment area.) Some consider it a point of principle to send their children to the local state school.

There is plenty of evidence showing that family background is a better indicator of future success for children than type of schooling. There is a strong case to be made that says mixing children from all walks of life in comprehensive schools is good for society and good for the individual child’s character and learning. That is pretty much the case that Ed Miliband made in his own conference speech when he advertised at length his attendance at the local inner-London comp. This was also, of course, meant as an implicit rebuke to the rarefied world of Eton College, where the Prime Minister was to be imagined in effete isolation from the gritty realities of urban Britain. (The differently rarefied world of Miliband’s upbringing at the heart of a liberal left intelligentsia is another story.)

There is a great danger for the Labour party in conflating disdain for the kind of school that David Cameron attended with the education policy he is overseeing; to think, in other words, that because many Tories are posh, their education policy is willfully and vindictively exclusive. Academies and Free Schools are state schools. The former evolved from Labour party policy, which was developed not out of some craven or treasonous urge to smuggle Conservative ideology into the party but because the Blair government had found the limits to what could be achieved in terms of raising standards in struggling schools by simply giving them money.

There are plenty of interesting arguments to be had about the merits and failings of Academies and Free Schools in both theory and practice. Does the exercise of parental choice really work as a lever for driving up standards? Does the creation of a “quasi-market” for schools somehow degrade the concept of a universal, state education? Do new admissions policies permit discreet or explicit selection by cultural, religious or ethnic characteristics and thus damage community cohesion? Does cutting back the role of local authorities diminish democratic accountability? Does Michael Gove’s model award too much central power to the Secretary of State? Etc.

But before Labour gets too bogged down in those issues, it needs a clear political response to the basic retail offer that David Cameron spelled out yesterday: the trappings of a private school, available to anyone, funded by the state.

Plainly, every academy is not going to turn into a local Eton or Winchester. Few will come close for fairly obvious reasons to do with money. The whole experiment might turn out to be an epic disaster. But in the meantime it would be naïve of the opposition to deny that the concept of a free, private-style school just around the corner is attractive to all kinds of voters – whether you call them “the squeezed middle” or “aspirational” or just plain “parents”.

Does Labour think that Cameron's offer of state schools that look like private ones is merely unrealistic or inherently despicable? Is it the ends of Michael Gove’s revolution that the opposition rejects or the means? Does it want to compete for political ownership of academies or will it gladly see them re-branded as a Conservative idea? Until there are clear answers to those questions, Labour isn’t seriously in the business of debating education policy, which will be a problem come the next election.