Two children suffered harassment and abuse after being moved next door to a family that engaged in persistently anti-social behaviour, the Supreme Court has heard.
Known only as CN and GN, the victims allege Poole council failed to protect them from harm between 2006 and 2011, despite knowing they were at risk.
CN - who is severely disabled - attempted suicide at the age of 12.
The case concerns whether authorities owe children a duty of care.
That includes investigating possible sexual, physical or emotional abuse and neglect, and taking remedial action.
Currently, the Criminal Injuries Compensation Authority award is capped at £500,000.
However, there is no other route to compensation for children whose needs can only be met by damages in excess of this sum.
The claimants brought a case against the council for breach of a common law duty of care derived from statutory duties under the Children Act 1989.
However, the Court of Appeal ruled against them last year.
At Monday's hearing before five Supreme Court justices, Elizabeth-Anne Gumbel QC said a number of claims against local authorities for negligently failing to remove children from obvious sources of danger had been successfully litigated or settled by agreement.
She added there were currently "a very considerable number" of outstanding claims.
"If the decision of the Court of Appeal in the present case is upheld, all of these cases will be struck out, leaving the children involved without an effective civil remedy," she said.
The appeal is supported by charities including Article 39, which fights for the rights of children and young people who live in children's homes, and the Care Leavers' Association.
The hearing is expected to conclude on Tuesday with judgment reserved.