They cost £25 million each to build. Their airy spaces inspire. They are, on average, three times oversubscribed. After shaky starts in some areas their GCSE results are improving twice as fast as the national average, and they get a fresh burst of endorsements in a booklet published today by the CentreForum think-tank. In it, Lord Adonis says of city academies that they are the future of secondary education, “and it works”.

It had better. This Government has committed itself to academies so deeply that it has committed its successor to them as well. Eighty-three have been built since 2005. Fifty more will open this year, 80 more next year and 100 more in 2010. As an infrastructure programme, but also as an educational innovation, academy-building already eclipses most initiatives of the past generation, and “academisation” is the likely fate of many of the 630 comprehensives identified by Ed Balls, the Education Secretary, as failing.

So far, so good. In three short years the academy model has confounded many of its sceptics. It has shown that new buildings, a fresh ethos, close sponsor involvement and, above all, independence from direct local authority control, can transform the chances and attainment levels of pupils previously ill-served by the worst urban comprehensives.

But the academy programme is in danger on two fronts. It is at risk - not suddenly, but gradually - of losing the very autonomy that distinguishes academies from comprehensives. As they become more widespread, the urge of Government is to exert greater control over them, deterring precisely the sponsors from businesses and universities that academies need to thrive. Ministers, meanwhile, are losing sight of this programme's most visionary goal, which is to transform secondary education not just for the underperforming few, but for the many.

Today's report calls for an acceleration of academy-building beyond the current target of 400. Even without such an acceleration, academies will soon teach more pupils than all those represented at the Headmasters' and Headmistresses' Conference of leading private schools. Almost all these pupils have moved from failing city schools to academies built specifically to replace them. Almost none come from comprehensives that are merely coasting.

Academies, in other words, are being used as costly, targeted tools to fix very specific problems. There is an unfashionable cross-party consensus that they could do more. Conservatives, Liberal Democrats and some Blairites within Government agree that a radical relaxation of rules on the supply of state-funded education would draw new providers into the academy system from both voluntary and private sectors. The Tories, in particular, speak of “an avalanche of philanthropy” worth billions of pounds, waiting only for guarantees of freedom from local authority meddling.

More and broader provision would make a reality at last of competition and parental choice. It would also bring closer this Government's holy grail of wholesale middle-class defection from private to state-funded schools. But it will only happen if those schools are truly independent in terms of staffing and curriculum

Such schools exist - in Sweden, where anyone can bid for public money for a school, and can profit from running it. They do not exist in Britain. Nor will any major party back the thorough deregulation of supply for fear of being branded privatisers. The Lib Dems come closest, but all should be bolder. More academies with more independence will not mean privatised education. It will mean choice for parents in Middle England as well as inner cities, and higher standards for all.