Mother-of-three "Ms A" lost her home in March 2014 when her housing benefit payment was cut and she could no longer afford the rent, The High Court heard.
Westminster City Council temporarily moved her to north London and tried to ban her from re-applying for a home in the central borough for 12 months.
A judge ruled the ban was unlawful.
The council, which has a long waiting list for social housing, offered her temporary accommodation in Enfield and said for 12 months it would register her with a private landlord instead.
However the family's lawyers argued the suspension on applying for social housing breached the 1996 Housing Act which requires councils to give homeless families "reasonable preference" for social housing.
Jayesh Kunwardia, from Hodge Jones & Allen solicitors, said: "This landmark ruling makes it abundantly clear that homeless people have the right to bid for social housing from the time they secure a full housing duty from a local authority rather than being suspended for one year."
Judge Peter Blair QC, sitting in London, said even without the ban the family, who had been living in Westminster for five years, may have a long wait to be allocated a permanent council home in Westminster because of the "high demand and very short supply."
He said "The waiting lists are so vast that on average people have a seven to 10-year wait before they reach a point high enough up on the register to have any realistic prospect of being successful in a bid."
A family in central London made homeless by the housing benefit cap was unlawfully prevented from registering for social housing, a court has ruled.