Christina McAnea, Unison spokeswoman on education, said the private sector had estimated the market in education services would be worth pound;5 billion by the end of the next Parliament.
But she warned: "To consider going down the route of handing over responsibility for a wide range of education services to private companies causes us grave concern. There's no natural market out thre.
"Companies are not doing it out of a philanthropic desire to improve communities, they are doing it because they see huge profits. We don't believe education should be privatised by stealth."
She suggested the Office for Standards in Education could develop early intervention teams to pick up on struggling education authorities before they fail.
Unison claims to be the biggest union in the education sector, with more than 250,000 members including classroom assistants and education authority officers.
More fringe reports on www.tes.co.uk