The leader of the opposition doesn't control much. But the one thing he has total power over is what he asks at prime minister's questions – which is why it was so revealing that last month Ed Miliband chose to attack the coalition government's free schools programme.

And if we were in any doubt about the depth and nature of his hostility, the script for his "spontaneous" rejoinders (which an aide left in a Commons lavatory) revealed all. According to the memo, free schools were "pet ideological projects", undeserving of public money. Miliband's loo paper confirmed that all schools had to be bog standard.

The truth, of course, is that there is nothing "ideological" about free schools – if by "ideological", Miliband means that supporters of these new schools need to subscribe to one particular world view. Public sector reformers across all political parties support free schools because they can see that they extend choice, generate innovation, challenge existing institutions to raise their game and promote higher standards.

Conservatives support free schools because they devolve power to Burke's little platoons. Liberals support free schools because they embody John Stuart Mill's vision of the state paying for universal education through schools run by autonomous bodies. Classical republicans admire free schools because their creation requires the virtues of independence of mind and a sense of civic obligation. Classical Marxists support free schools because they embody the ideal of the soviet, a self-managing institution run by workers in the wider public interest – which has been tried from Petrograd in 1917 to Venezuela today. Free schools have won support right across the political spectrum, from Andrew Adonis and Tony Blair to Nick Clegg, Vince Cable, David Cameron, John Redwood and Nigel Farage.

Given the breadth – and philosophical depth – of the support for free schools, your ideology would have to be remarkably rigid to oppose them. But, unbelievably, that is the current Labour leadership's position. Ed Balls, the shadow chancellor, opposed the legislation that allowed them to be set up. His successor Andy Burnham, the shadow health secretary, called free schools "freaky schools". Miliband has said are the opposite of what we need. And in June Stephen Twigg, the shadow education secretary, confirmed there would be no more free schools under Labour – and hinted ominously that existing free schools would have their freedoms curtailed.

My approach to education reform is the opposite of Labour's. It's rooted in evidence, not ideology. I believe in following the Blair dictum: what's right is what works. Everything I am doing is driven by getting more children – especially the poorest children – to succeed academically, which is why I published a new draft national curriculum last month that makes greater demands of both students and teachers. Leftwing academics previously described the new curriculum as asking "too much, too young". But the evidence shows that children benefit from high expectations and a knowledge-rich curriculum, and I want more children to enjoy the type of education the rich and well-connected have always secured for their own.

So the reason I back free schools – and the reason why the Labour leadership's ideological opposition is so perplexing – is that all the evidence shows free schools are driving standards up across the board. They are proving a remarkable success, and remarkably popular.

Ofsted has just completed its independent inspections of the first 24 free schools, which opened in September 2011. The results are in – and these schools are outperforming the rest of the country. The proportion that are good or outstanding outstrips other state schools. Although a handful of schools required some improvement when judged against Ofsted's tough new inspection framework, the leaders of those schools are already taking action to ensure they improve – or are ex-private schools that need a little more time to adjust to the disciplines of state school inspection.

For any group of 24 schools, these inspection results would be a cause for celebration. If a single local authority performed this well, we would applaud its commitment to excellence. But these schools have had no external support from local authorities or political sugar daddies. In fact, Labour politicians tried to strangle them at birth, seeking to deny them planning permission and using every Tammany Hall trick it could to prevent their arrival. As a result, some of these schools had to open in second-choice, or even third-rate, buildings. Others have had to put up with adverse publicity from campaigners whose own failures had been overlooked for years.

These schools have been set up and run by dedicated groups who believe in extending educational opportunity, including many parents and teachers. They can choose to open for longer; offer academic and other courses unavailable in other local schools; and hire the best people to teach, irrespective of union-imposed dogma. They are directly accountable to local parents because if they fail to offer a good standard of education, they won't attract students and will therefore close. But by offering parents a higher level of ambition, almost all are oversubscribed after – at most – two years of operation.

There is much to celebrate in our state education system at the moment – the best generation of young teachers ever, the best generation of heads, and more schools being judged good or outstanding in inspections. Free schools are now an integral part of the growing success story of state education in England.

Their success reflects incredibly well on the teachers who work in them, the comprehensive ethos that pervades them, and the parents who support them. I only hope that – as he reflects this summer on what a new politics should look like – Miliband will accept that acknowledging he's been wrong about free schools would be a great first step.