Colin Sleate, 29, was jailed for life at Nottingham Crown Court last week after a trial in which the jury was told that the girl suffered 107 external injuries.
Family and neighbours had alerted social services to their concerns about the treatment of the child by Sleate and her mother, Tina White, six months before her death in November 1992. Sentence was adjourned on White, 22, who was convicted of manslaughter.
The trial judge, Mr Justice Tudor-Evans, called for the full details of a confidential social services inquiry to be made public.
He said: 'What is described in the report is appalling. I think in a case like this there should be no sweeping under the carpet.
'I do not have the power to order a public inquiry, but I shall write to the appropriate minister and ask for an inquiry to take place.'
The report, details of which have been leaked, says: 'The failure of social services staff to fully investigate the facts and their failure to report the matter to the police is at the heart of this tragic incident.
''A thorough investigation of the facts that were reported in the referrals concerning Leanne was not undertaken.'
Among the errors noted was the inability of social workers properly to fill out Child Protection Forms about the concerns expressed to them by neighbours in Hucknall, Nottinghamshire, where Leanne lived.
Among other errors was the mis- spelling of Sleate's name, which, combined with a failure to record his date of birth, could have led to problems when checking police and probation records, the investigation found. Another serious omission in Leanne's file was the failure to record the name of the social worker who made the first visit to her home in June 1992.
Social workers are said to have made no 'systematic gathering of information' - resulting in 'no clear picture of Leanne, her family situation or environment'.
As a result, the investigation has found that complaints including some from Leanne's grandmother, Mary White, were viewed 'in splendid isolation'.
Three contacts were made with social services by early July 1992 and there should have been a far fuller investigation, the inquiry concluded.
The report noted: 'Work appears to have been unstructured and not geared to fully investigating the concerns about Leanne, which by this time we feel ought to have been sufficient for a primary care discussion to have been called, if not a case conference.'
At both the initial home visit in June and subsequent visits, social workers failed to examine Leanne to check for injuries.
As a result, the report states: 'It was impossible in our opinion to form a view of Leanne in the context of the referrals received without examining her.'
Social workers also failed to take the names of neighbours who had voiced concern about Leanne.
Because of the errors, Leanne's condition was never thought serious enough for the matter to be referred to the police.
The 20-page report into the case, which recommends 28 changes to the handling of child abuse allegations, is being considered by Nottinghamshire's social services director, David White.
Angela Lambert, page 14