The vast majority live in bed and breakfast or temporary accommodation with their families. Homelessness has terrible consequences on schooling, creating more problems for the already disadvantaged, says the charity.
Shelter figures for 1998 are not yet available but are expected to tell a similar tale.
The report, Growing Up Homeless, reveals:
* Two-thirds of families in temporary accommodation had to move their children between schools as a result of a change of address; * The introduction of performance tables means schools are often unwilling to spend time on homeless children, who are more likely to have emotional and behavioural problems; * Homeless children lag behind in literacy and other basic skills; * Homeless children are treated as outsiders by other pupils, which can lead to bullying.
A spokeswoman for Shelter said: "A lot of the people who come to us are having real problems getting and keeping their children in schools. The children are suffering because of it.
"A lot of our clients are saying the effects of homelessness on children's education are not recognised by schools as a specific problem. The potential for moving around children in temporary accommodation is very great and therefore the potential disruption to their education is even greater."
The Shelter report coincides with research by the Scottish arm of the charity which shows 24,000 children under 16 are homeless north of the border.
The Scottish survey, carried out by the Institute for the Study of Education and Society at Edinburgh University, concluded that councils needed to have better links between education, social work and housing departments. Some schools admitted that they were unaware pupils were homeless because there was no formal reporting system in place.