Pauline Bossa, a Zairean, and Cynthia Nyembe, from South Africa, are both currently having their political asylum claims considered by the home office. They are receiving no state benefits and do not have money even to buy food.
Both women were told by Brent in November last year they were being sent to live at a women's hostel in the Sussex seaside resort.
But, when they got there, they say the accommodation on offer was 'entirely unsuitable', with no privacy in the dormitories, a dire lack of storage space, and only one kitchen, toilet and shower for 20 residents.
Their lawyers claim Brent is in breach of its duties under the 1948 National Assistance Act to provide them with the basic necessities of survival, including a roof over their head.
Mr Justice Latham was told the women's lawyers had written to the council seven times since November, without response.
But the judge allowed a short adjournment of the case so that the council can have its say. The case is now due to return to court on February 17, before the same judge.
The women, both of whom say they fear persecution or torture if sent back to their homelands, each spent more than a year living in London before Brent sent them to Hastings.
They say the council took no account of the roots they had put down in London and that a move to Sussex would take them away from little support they have.
The women spent just one night at the women's hostel in Hastings before returning to London.
Both have refused to go back to Sussex, and Brent LBC, which formerly paid their rent and provided them with food, has withdrawn all their support.
Unless the dispute is resolved in the meantime, the case will return to the high court on February 17 when the women will seek permission for a full judicial review.