The MPs' report, The role of private-sector organisations in public education, says: "We do not consider that private-sector organisations are inherently more skilled or are more likely to achieve high standards than public-sector organisations."
It says the best mix would take private-sector management expertise and public-sector education skills. But successful councils are unable to bid for contracts to run failing authorities because of the punitiv penalties attached to missing targets, MPs say.
They recommend allowing experienced LEA officers to help under-performing councils, backed by a "cadre" of top state education administrators.
The report came out as Benno Schmidt, the founder of the high-profile private US education firm Edison Schools, returned to the UK to press the case for privatisation.
The firm runs 80 schools with 38,000 students in the States and says is keen to consolidate after floating on the stock market. Mr Schmidt, a former president of Yale University, has told MPs in the past that he could reduce class sizes and give each pupil a laptop at no extra cost to the taxpayer. He regards schools as the last of the cottage industries.