Westminster City Council challenged the refusal by the Home Office's National Asylum Support Service to accept responsibility for asylum seekers with special needs.
The ruling suggests councils will have to pay for any costs other than basic accommodation.
Westminster claimed costs, over and above the existing grant system, to meet the needs of a woman being treated at St Mary's Hospital, Paddington.
The council insists she needs accommodation close to the hospital, but now has to cover the cost.
A spokeswoman said: 'We challenged the government's refusal to accept responsibility for asylum seekers with special needs. We put her in accommodation near the hospital because of her disability, but NASS [the support service] were not willing to pay.'
A spokeswoman at Kent CC said the decision could have far reaching consequences for councils where there are large numbers of asylum seekers.