Reports on Cambridge Education Associates in Islington, north London, and CfBT, a not-for-profit organisation in Lincolnshire, come as rare pieces of good news about the Government's beleaguered local authority education privatisation programme.
The Hull university research was based on questionnaires sent to all headteachers in the two authorities.
In Lincolnshire, the proportion of positive responses to questions varied between 83 and 96 per cent and in Islington between 96 and 100 per cent.
Brent Davies, one of the authors, said he had not expected support to be so high, particularly in left-leaning Islington.
"Heads as a breed tend to be quite sceptical," he said. "They had total confidentiality and could have slagged these companies off if they had wanted to. Surprisingly they didn't. I think the reason seems to be because they are now allowed to get on with their jobs."
The two-year research study was commissioned by the National College for School Leadership in conjunction with the two companies, who won contracts for the work.
It asked heads about the quality of school improvement work, training courses and the speed of response to questions raised with the companies.
The only blip was about the effectiveness of a recently-introduced electronic school development planning system, about which only 52 per cent responded positively.
The research also asked heads to compare their relationships with CfBT and CEA, and those with central government. They were questioned about which allowed them the most freedom, flexibility, support for innovation, risk-taking, and which held them the most accountable.
CfBT came out higher than the Government in every category except accountability. In Islington, CEA finished higher in allowing more freedom, innovation and accountability.