If Ed Miliband was nervous before his "One Nation" conference speech, he at least knew that a few lines were guaranteed to attract the desired response from his audience. Like “Michael Gove”.

The pantomime boos that greeted Miliband’s mention of Gove’s name showed the animosity Labour holds him in. But while criticisms of Gove’s policies as Education Secretary might be an expedient way of getting a few cheers, they miss a deeper point. Whatever the merits of Gove’s solutions to British education, he is at least right in his underlying diagnosis that something isn’t working. The attainment gap between private and state education is the highest in Europe.

Labour’s educational policy is much better known for what it opposes – above all, Gove’s free schools - than what it actually supports. The party’s policy on academies, the centerpiece of New Labour’s education reforms, remains somewhat confused. This had better change, and fast: while both Labour and the Conservatives exaggerate the significance of free schools, academies are where Gove’s true radicalism has been. After the last election, there were 203 academies; there are now 1957 (compared to 79 free schools). Labour needs to outline exactly how it would deal with these new academies and indeed formulate its vision for education in this country. Miliband’s outlining of plans for “the forgotten 50 per cent” is certainly a positive step. But there remains a fundamental problem: Labour needs to lay out coherent ideas for how to improve state schools when substantially greater investment isn't deemed a viable option.

For inspiration, Labour needs only to turn to the NHS. As schools do, the NHS has to compete with private alternatives. Why do the public have a better perception of state hospitals than state schools? One of the reasons is that, while the best teachers can move away from the state sector that is not true of the best doctors – the principle that those who work in the private health sector must also contribute to the NHS helps mitigate differences in the quality of care provided in the two. Doctors have been state-subsidised to do their degrees (as is still the case under the new tuition fees) and it seems only right that their skills should benefit all, not just those who can afford it.

The idea is, perhaps, the very embodiment of "One Nationism" at work. And it could relatively easily be mimicked where schools are concerned, mandating that all teachers spend at least half their career in the state sector.

For all the life advantages private schools give their pupils only so much can be apportioned to simply better facilities. More than anything, parents pay for the best teaching; and, while there are many excellent teachers in the state sector, a disproportionate number of the best teachers are at private schools. A sensible policy to amend this would provide a compelling vision of how Labour plans to improve the quality of state schools.

This could be accompanied by asking more of private schools in return for their charitable status. While opening up school playing fields is a worthy idea and should be extended, there is ample scope for more imaginative thinking: for instance, mandating that private schools invite pupils from nearby state schools to special classes for Oxbridge candidates.

Labour can't allow its educational policy to be caricatured as being mere defenders of a status quo that isn't working. Just as investment provides no guarantee of tangible improvement in education, so a shortage of it needn’t stop state schools getting better. Indeed, an absence of money has actually created a climate rifer for radical educational ideas. As Labour proclaims to speak for "One Nation" it needs to be proposing them.