The report said 500,000 children in the UK have been exposed to such abuse, BBC wrote.
But there are warnings that escaping violence can mean families struggling to get children into another school.
The report, from two charities — Hestia and Pro Bono Economics, also estimated that domestic violence costs public services up to £1.4 billion per year.
The report wanted the Domestic Abuse Bill, published by the government earlier this year, to be amended to make it easier for victims of domestic violence to get into another school if they have to move address.
The bill is intended to give more support to the victims of domestic violence.
But the charities want more attention paid to the consequences for children who will have seen acts of violence and might have to take shelter elsewhere.
They want priority for school places for these children, as is given to children in care or adopted from care and some children with special needs.
If families are in refuges, the charities want local authorities to provide a change of school within 20 days.
At present, Lyndsey Dearlove, of Hestia, said, children might be waiting from four to six months for a place and many families might have to be move several times before getting a more permanent new home.
"For too long children have been overlooked in the response to domestic abuse, seen merely as 'witnesses' rather than children who have experienced deep trauma and crisis. This must change," said Dearlove.
"We need measures put in place to support children early on and break the cycle of abuse," she said, on behalf of the charity, which provides shelter for victims of domestic violence and human trafficking.
The report also highlighted how domestic violence causes other difficulties in children, such as mental health or behavior problems.
And it said the annual cost to taxpayers could be up to £1.4 billion: £790 million in extra costs for education services, £460 million in foster and residential care, £110 million in crime and £70 million in health care.
Former cabinet secretary, Lord O'Donnell, who chairs Pro Bono Economics, said, "Children exposed to domestic abuse suffer in the short, medium and long-term.
"As a society, we have a moral imperative to ensure protection from the immediate risk of such trauma but also to provide support whenever unfortunately such exposure should occur.
"While these numbers are striking, and this report timely, there is always a need for more robust evidence with which we can enhance our understanding of such issues, from causes through to effects and solutions."
A spokesman for the Department for Education said the school admissions code required councils to have ‘fair access’ rules, in which the most vulnerable children should be offered a place ‘without unnecessary delay’.
There is also a review of support for ‘children in need’ and the department said it was considering changes for those families seeking places during the school year, including those in refuges, so that they could get a "new school place as quickly as possible".