If you want to influence Labour’s education policy, you could do worse than target a think-tank and a management consultancy. More than London university’s institute of education, the teaching unions or even the Labour party, the Institute for Public Policy Research and McKinsey have the ear of people in high places.

McKinsey’s motto, “Everything can be measured and what gets measured gets managed”, could apply to Labour’s schools policy.

As the chart (right) shows, the web of connections between 10 Downing Street and McKinsey is rivalled only by that between the IPPR and the Department for Education and Skills.

David Miliband, the former schools minister, started out at the IPPR and all four special advisers to Education Secretary Ruth Kelly - Richard Darlington, Will Paxton, Dan Corry and Gavin Kelly - are ex-IPPR (although curiously none specialised in education). Nick Pearce, director of the IPPR, is a former special adviser at the DfES and Home Office.

Relations between the two bodies are close enough to allow IPPR research fellows to moonlight in Labour’s innovations unit, and for Anna Bush, a DfES civil servant, to be seconded to the think-tank where she wrote a report expected to criticise the Government for not doing enough to get the best teachers into inner-city schools.

The think-tank - which recently argued for a limit on fixed-term exclusions - also has links with No 10 where Matthew Taylor, Mr Pearce’s predecessor, now works.

Other think-tanks also have influence. Philip Collins, who became the Prime Minister’s public services guru after May’s election, was until then director of the Social Market Foundation where he proposed a lottery for places at oversubscribed secondaries.

Tom Bentley at Demos is another who has seen government from the inside as a DfES special adviser during the Blunkett years.

Those who have moved between think-tanks and government say the two are complementary. Working in a think-tank allows advisers to build expertise in a policy area which is invaluable in government. Conversely, think-tank people with Whitehall experience have a better idea of how policy is formulated and how their ideas will affect government.

The advantage of outside experience within Whitehall is increasingly recognised within the civil service with Sir Alan Wilson, former Leeds university vice-chancellor, and Michael Stephenson, former director of factual and education programming at the BBC, both on the DfES board.

Insiders insist such relationships are far from symbiotic, with even sympathetic think-tanks frequently infuriating ministers.

But the IPPR, SMF and others are in regular discussions with government advisers about policy and are sometimes happy to act as outriders on some issues, helping to start controversial debates and fly political kites without ministers getting their hands dirty.

McKinsey, the global consultancy closely associated with the failed US energy company Enron, is, if anything, even better connected to Downing Street. David Bennett, a former partner at McKinsey, now heads the Downing Street policy unit.

Until he quit this month to avoid allegations of a conflict of interest, Lord Birt, Blair’s “blue skies thinker”, was also working for the consultancy.

And Michael Barber, until this month head of the PM’s delivery unit, will take up a job at McKinsey this autumn.

Professor Barber, a former National Union of Teachers education officer and more recently head of the DfES standards and effectiveness unit, is one of the few key figures with a background in education.

Another is Sir Cyril Taylor, chairman of the Specialist Schools Trust (see box, right). Along with Conor Ryan, Tony Blair’s new education adviser, and his predecessor Lord Adonis, now the schools minister whose influence on the PM is hard to overstate, Sir Cyril makes up a powerful Blairite trinity, pushing parental choice, school autonomy and private-sector interest in state education.

Indeed, Lord Adonis’s recent move from Downing Street to the DfES’s Sanctuary Buildings headquarters was a sign of the PM’s determination to tighten his grip on education policy after the Charles Clarke years when the then education secretary and his deputy Mr Miliband had shown a willingness to stand up to No 10.

Blairites felt Mr Miliband’s working relationship with those unions who signed up to the workforce deal, particularly the NASUWT and the Secondary Heads Association, had become too cosy. That is unlikely to happen with Lord Adonis, however.