A major sponsor of the academies programme has called for the extension of the controversial scheme to tackle under-performance in primary schools, where he claims "extraordinary complacency reigns".
Paul Marshall, co-chairman of the charity Absolute Return for Kids (ARK), says state-funded independent schools are needed to introduce new ideas into the primary sector.
Mr Marshall and ARK have so far launched three academies and have another 12 in the pipeline.
In a book, Academies and the Future of State Education, published this week by the Centre Forum think tank, he describes government figures, which suggest a much smaller proportion of primaries are "failing" or underperforming than secondaries, as "statististical hogwash". Mr Marshall, a millionaire fund manager, claims far too few primaries manage to overcome pupils' social disadvantage at an early age, when, he says, it should be easiest.
"The importance of tackling poorly performing primary schools is reinforced by a large body of evidence showing that a child's educational prospects are largely determined before they arrive at secondary school," he writes.
Mr Marshall says the solution is to allow primary-age academies.
"Greater diversity of primary provision would intensify the debate about what works best for disadvantaged children in their early years," he says. "We would no doubt see more outreach to parents, more experimentation with numeracy and literacy programmes and a greater quest for solutions to poor behaviour." As well as encouraging more contact with parents, he believes primary academies could actually be run by them.
He says that parent-run schools would be helped by removing the need to find sponsorship fees or build a new building.
"Primary schools are smaller and much easier to manage than secondaries," Mr Marshall writes. "It should be perfectly acceptable for parents to group together to establish their own schools, particularly when their existing one is threatened with closure, as is the case with more than 300 rural schools."
Mr Marshall also believes primaries could be key to switching the academy scheme from allowing sponsors to take over failing schools to letting them establish new ones.
In another chapter, Julian Astle, from Centre Forum, argues that this extra capacity would increase competition and raise standards.
Mr Astle, once an adviser to Paddy Ashdown, the former leader of the Liberal Democrats, says his idea, inspired by the Swedish school system, could be funded by expecting sponsors to meet capital costs but allowing them to make profits.
The Government is preparing to launch a new improvement plan for underperforming primaries in the autumn. So far, there's been no suggestion that this will involve academies serving primary age pupils.
But, writing in the same book, Lord Adonis, the junior schools minister, says he will be looking closely at existing all-age "all-through academies" for pupils from 3 to 18, to see if the idea should be applied to more schools.
In another chapter, Richard Gilliland, who in September will become executive head of an all-through academy in Lincoln, argues it will be a "win-win situation". Primary pupils will benefit from secondary expertise in specialist subjects while the primary involvement will give secondary age pupils "an environment which makes young people feel more comfortable".
'Academies and the Future of State Education', edited by Julian Astle and Conor Ryan.