The report by domestic violence charity Hestia and economics charity Pro Bono Economics says that early intervention is needed for this group of children due to the severe effect witnessing violence in their home has on their mental health, schooling and life chances.
It estimates that around 500,000 UK children have witnessed severe domestic violence. Of these, between 35,000 to 100,000 are at risk of developing an emotional or behavioural disorder as a result of their experience.
This leaves them at greater risk they will become involved in crime, be placed in care, need mental health support as an adult and specialist support in school.
In addition, their education is more likely to suffer if they are forced to move areas due to domestic abuse.
The report estimates that the cost to the taxpayer by the time these children reach the age of 28 is between £500m and £1.4bn. This includes up to £460m in care costs and £790m in education costs, such as special needs support.
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The report calls for amendments to the government's Domestic Abuse Bill, which was published in January, to ensure children are prioritised for early health support, particularly regarding their mental health.
Children in refuges and those who have had to move due to domestic abuse should be given priority access to school places. A legal duty should also be placed on councils to ensure they respond to a change of school request from children in refuges within 20 days.
In the report, Hestia chair Terrie Alafat states the effect of witnessing domestic violence "can be catastrophic and last a lifetime".
"Our frontline case workers have told us devastating stories that reveal the immediate cost to children," he states.
"One 12-year-old boy, living at a refuge in south London, was unable to go to school locally and had to travel through two boroughs to return to his school. He has since been groomed by gang members on his journey to school."
Lyndsey Dearlove, head of Hestia's UK Says No More domestic abuse and sexual violence prevention campaign, said: "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. We need measures put in place to support children early on and break the cycle of abuse. The Domestic Abuse Bill is a once in a lifetime opportunity to make this a reality."
Pro Bono economics chair Gus O'Donnell added that more evidence is needed to better understand the effect of domestic abuse on children.