Anntoinette Bramble, chair of the Local Government Association’s children and young people board, said: “This report reflects the concerns we have been raising for some years.
"While we believe a mixed market of provision of homes for children can be positive, our members are increasingly concerned about the growth and market share of the very largest providers.
“We are increasingly hearing of harrowing cases where suitable homes cannot be found for children, including those with complex needs, who desperately need help. This is unacceptable and as a country, we must do better."
The CMA will publish a final report in March, which is likely to suggest ways local authorities can work together to increase their bargaining power.
A Department for Education spokeswoman said: “Councils are responsible for ensuring sufficient places to meet the needs of children in their care, including by commissioning places from private or voluntary sector providers as required. They are also responsible for agreeing prices with providers accordingly.
“We will be investing £24 million to start a new programme to maintain capacity and expand provision in existing secure children’s homes, so that there are more high quality, safe homes for vulnerable children as well as making up to £19.5 million capital funding available for councils to develop new homes.
“The Independent Care Review will also address the sector’s major challenges as part of its wholesale review of children’s social care.”