However, lawyers said that children might be able to apply to social services departments for housing under the Children Act. The courts have yet to determine this issue.
Yesterday's judgment came as campaigners accused councils of failing to carry out their duties under the Act to house children in need.
The first case heard by the five law lords centred on an application made on behalf of Moses Bentum, five, of Bexley, south-east London, after his mother and father, political refugees from Ghana, had been refused a council house. The local authority said that they had deliberately made themselves homeless by failing to keep up mortgage repayments.
In a second case, an application was made on behalf of Graham Garlick, also five, after his single-parent mother was evicted from her council flat in Oldham, Greater Manchester, for running up rent arrears of pounds 150.
Giving judgment, the law lords unanimously upheld a Court of Appeal decision that neither council had a duty to house dependent children whose parents had already been turned down.
Four of the law lords thought that similar arguments applied to a third case, in which a woman lacking hearing, speech and education claimed the right to a council house. She did not have the understanding to make an application in her own right, and was therefore dependent on her family. Lord Slynn, disagreed.
Russell Campbell, a solicitor with the housing charity Shelter, said: 'Although it's not surprising that the children have been refused, it's very sad that the mentally-ill have been ruled out.' However, he pointed out that children no longer dependent on their parents, for instance those fleeing sexual abuse, had to be housed.
A report published yesterday by the homelessness charity, Centrepoint, claimed that the majority of councils in London were failing to fulfil duties imposed under the Children Act to house homeless teenagers.
Section 20 of the Act places a duty on local authorities to accommodate 16 and 17-year-olds whose welfare is likely to be seriously prejudiced without the provision of such a service.
The Children Act itself is also failing to meet the needs of young people who have left home or council care. 'Insufficient resources and overly strict criteria for assessing need are the main causes of failure,' the Centrepoint report says.
Launching the report yesterday, Centrepoint called for a London-wide strategy to assess needs and develop facilities, and for extra government funds for councils.
Nick Hardwick, its director, said: 'Homelessness is a shameful and degrading experience but the people who should be ashamed are not the homeless but the rest of us. We are one of the richest countries in the world. The fact that so many 16 and 17-year-olds, still legally children . . . are on the streets should be on the conscience of us all.'
Research for the survey, commissioned by ITV Telethon, was conducted in 32 London local authority social services departments. It found:
Over half had not developed policies and procedures to assess homeless young people, under section 20.
A total of 77 per cent said they did not have accommodation to meet the needs of homeless 16 and 17 year-olds.
And 44 per cent did not consider homelessness alone as a sufficient condition to provide accommodation.
Housing our Children: The Children Act 1989; Centrepoint, Livonia St, London, W1; free.
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