A High Court judge is to investigate after three sisters all aged under 10 developed a sexually transmitted infection.
Abuse concerns emerged after the children's parents had twice been evicted from different homes and the family spent a month living in temporary accommodation arranged by council staff.
Early in 2018, the family spent two days in a hotel, two weeks in a caravan in Southend, Essex, and two weeks in a caravan in Lincolnshire.
Social services bosses with responsibility for the children, who are now in foster care, began family court litigation nearly a year ago.
A family court judge considered the case at private hearings in London and concluded that the girls' father might have caused the infection.
The father appealed against that finding and detail of the case has emerged as a result of three Court of Appeal judges examining issues at a public Court of Appeal hearing in London in late March.
Lord Justice Peter Jackson, Lady Justice King and Lord Justice Lindblom have now said, in a ruling, that they are not satisfied with the family court judge's finding.
They say a judge based in the Family Division of the High Court in London must take charge and review the case.
Appeal judges told how the sisters and their parents moved in and out of London in recent years.
They said the family had been known to social workers for nearly a decade.
The family lived in Haringey, then moved to Islington, and were evicted during the summer of 2017.
They found accommodation in Thurrock, Essex, but were evicted again in February 2018.
Staff at Thurrock Council then found them temporary accommodation - the hotel and two caravans - and in March 2018 they moved back to London to live with friends in Brixton.
The girls tested positive for a sexually transmitted infection during the summer of 2018.
Appeal judges said staff at Islington Council now had responsibility for the children and had begun litigation.
They have not identified the family in their ruling.