Local authorities are being urged by a cross party group of MPs to stop moving babies between foster carers.
Stability in a baby's first year is crucial, campaigners argue
The British Association of Adoption and Fostering says about one in eight children aged under two in England were moved three or more times last year.
A number of MPs have signed a Commons motion stating no baby should be moved more than twice in its first year.
The BAAF says stability during a baby's first 12 months is essential for good educational and emotional development.
The group reports that some older children have been relocated 20 times during their time in care over a number of years.
It wants local authorities to do more to streamline the system, so that babies can be adopted by the families already temporarily fostering them if their natural mothers decide to give them up.
Earlier this week, the BAAF, in launching National Adoption Week, said England was facing a "huge shortfall" of foster carers.
It urged more people to adopt, saying: "Many children in public care have suffered abuse or neglect and all are in desperate need of stability."
Some 4,000 of 78,900 children in public care in the UK are waiting for adoptive families, the association said.
It has launched a billboard campaign for adoption week, which runs until Sunday.
The billboards read: "This poster has no permanent home. Like thousands of kids in care, this poster will be moved again tomorrow."
BAAF said: "As the billboards are moved from place to place, they will become increasingly damaged - mirroring the harm caused to children moved too many times."