Ofsted and the Commission for Social Care Inspection published their annual joint report on the performance of local authorities in England, which rates their services for children.
This found that almost three-quarters provided good social care for young people. Seven local authorities - Camden, Tower Hamlets and Wandsworth, in London, Knowsley, Gloucestershire, Shropshire and Worcestershire - achieved the top "outstanding" grade in all categories.
But in 23 of the 102 authorities assessed, social care services were judged to be only adequate. And four authorities - Cornwall, Nottingham, Stoke-on-Trent and the Isles of Scilly - provided inadequate services for looked-after children.
Ofsted said that more than 5 per cent of children in care did not have a social worker, a fractional improvement on last year, but a higher proportion than in 2004. Stoke-on-Trent was identified as one of the councils which had failed to provide sufficient social workers.
Sheryl Burton, of the National Children's Bureau charity, said: "The social worker is the person responsible for assessing children's needs, helping them navigate their way through education, and talking to them about their future.
"Coming into care is a tremendously traumatic experience. It's hard enough with a social worker. Without one, it makes life far more complicated. It could mean that needs aren't being met, that children just feel miserable and lost."
Inspectors also highlighted the widening academic achievement gap between looked-after children and other pupils. In a third of councils, fewer than half of looked-after children left school with a single GCSE.
Inspectors raised a range of concerns about Nottingham's support for children in care, including their academic achievement.
"The stability of placements for children has been variable," they said.
"Children's homes have not always kept children and young people safe, and there have been increased incidents of bullying."
Nonetheless, in England there has been an overall reduction in the number of children moving between placements more than three times a year.
Christine Gilbert, Ofsted chief inspector, said: "The educational attainment of looked-after children is still a long way short of the level achieved by all children, and is improving only slowly."
Research by the National Foundation for Educational Research, reported in last week's TES, has shown that one in five primaries and one in 10 secondaries has no policy in place to support looked-after children.