The TES learnt of the details this week after Ed Balls, the Children, Schools and Families Secretary, asked the Prime Minister's delivery unit to conduct the review.
Mr Balls has been anxious to play down any suggestion that the review signals a reversal of what was Tony Blair's flagship education policy.
But the news that relations with local authorities will be in the spotlight has lent credence to suggestions that the academies programme is shifting away from its original emphasis on independence from the rest of the state system.
This week, Mr Balls told Parliament: "I want to bring them back into the mainstream."
More and more local authorities are sponsoring academies and Mr Balls has reduced their freedom over the curriculum.
He has also encouraged more public sector sponsorship by dropping the need for universities and schools to find pound;2 million per academy.
The TES has learnt that the eight-week Downing Street review, focusing on how well the programme is serving the needs of the most disadvantaged, will look at five individual academies in detail.
This emerged during a difficult week for Mr Balls, with Lancaster University research concluding that major government education reforms costing pound;3 billion had had a "meagre" impact on schools' exam performance - with its specialist schools programme particularly at fault.
The study also questioned the impact of competition between schools and the Excellence in Cities scheme.
But it did find that the Government's policies have had a more significant effect on the grades of pupils from poorer backgrounds, suggesting that the direction of resources towards disadvantaged pupils may be paying dividends.
The Schools Secretary became the first education minister to face a quick-fire "topical questions" session in the House of Commons this week, but put in a performance that failed to impress the sketchwriters.
He was saved by the Speaker of the House from having to respond when Michael Gove, his Conservative opposite number, suggested that he had actively encouraged Labour backbenchers to revolt against Tony Blair's trust school reforms.
Mr Balls recovered some ground during the debate on the Queen's Speech on Wednesday when he revealed a Tory "U-turn" on 14-19 reforms.
He contrasted support from George Osborne, the shadow chancellor, in 2005 for an "over-arching diploma that brings together academic and vocational training" with Mr Gove's warning that the latest three diplomas will undermine academic excellence.
17,000 sackings, page 9.