The charity found that 47 per cent had experienced at least one change of school since coming into care. One in five had experienced two or more changes and one in 20 moved schools at least four times.
Robert Tapsfield, its chief executive, said: "Children coming into care have a hard enough time without having to cope with a school move. For those who get moved time and time again, it's hardly surprising they fail to match the achievements of children from more stable backgrounds." He said more than 10,000 extra foster carers were needed to ensure greater stability in the lives of children in care.
"More foster carers will make it more possible to find children foster families who are right for them and who live locally. Fostering services that are prepared to pay and support carers properly have shown that it is possible to recruit the foster carers they need."
There are some 50,000 children and young people living with 37,000 foster families in the UK.
A separate report from Bristol university published this week found around half of parents with learning difficulties have their children taken into care. It argues that many of those families could stay together if the parents were given sufficient support, but that some social and health workers have a "negative attitude" to them.
The study Finding the right support? A review of issues and positive practice in supporting parents with learning difficulties and their children also recommends providing such parents with easy-to-understand information on all areas of parenting.
Professor Linda Ward, co-author, said: "We hope as a result of this study more parents with learning difficulties will be given the right support, so they can be good parents to their children and stay together as a family."