For example, when the children were asked if one could stop being British some said it was possible "if you went and lived in another country and learnt their ways" - a view which suggested that being British meant behaving in a particular way. Some were also confused about whether black people were British.
The survey was published in Educational Studies this week, as the controversy surrounding a top curriculum adviser's speech on fostering a British identity intensified.
Dr Nick Tate, chief executive of the School Curriculum and Assessment Authority, said that at a time of rapid social, economic and technological change, it was important for young people to have a secure sense of their cultural identity. Schools needed to combat the kind of cultural relativism which implied that it is possible to choose from an array of values and traditions.
He said that schools should foster a common culture for children, whatever their ethnic background. "There is a mistaken notion that the way to respond to cultural diversity is to try to bring everything together into some kind of watered-down multiculturalism," he said. "The best guarantee of strong minority cultures is the existence of a majority culture which is sure of itself, which signals that customs and traditions are things to be valued and which respects other cultures."
He said many people lived happily with more than one identity, and schools should respect and develop both.
However, Carrington and Short said that while many Afro-Caribbean and Asian children in their survey described themselves as having a dual national identity, fear of rejection, rather than pride in their cultural heritage may have been the reason.