Miss Julie Williams, 25, was refused help after the council decided in April that she had made herself intentionally homeless by deliberately allowing her children to damage their former privately rented house in Chatham.
Mr Justice Laws granted Miss Williams an injunction requiring the council to continue to provide accommodation for her until her case has been decided.
Miss Williams is currently living in two bedroom bed and breakfast accommodation provided by the council in Strood, Kent with her children (7,6,4 and 3). They have stayed there since last November.
Giving leave to seek judicial review of the council's decision the judge said if a mother did not control her children so that they caused damage in this way, it could amount to a deliberate omission which would be enough to deny them the right to be rehoused. But if Miss Williams had not been made to realise that this issue was central to the council's decision, she might have a case that she had not been treated fairly.