The government announced the inquiry in July, after renewed questions about what happened to an alleged dossier of claims made against a number of lawmakers and other figures in the 1980s.
"We found nothing to support a concern that files had been deliberately or systematically removed or destroyed to cover up organised child abuse," said the report by Peter Wanless, the head of children's charity the NSPCC.
However, the conclusions added: "It is very difficult to prove anything definitive based on imperfectly operated paper records system at 30 years remove."
But they took on new significance following revelations about late BBC presenter Jimmy Savile, who it is now believed to have been a prolific sex offender for decades without being caught.
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The rumours focus on a dossier that late lawmaker Geoffrey Dickens said he compiled in 1983 with allegations against MPs and other public figures, but of which no record remains.
Claims of a cover-up were fuelled after the interior ministry admitted earlier this year that it had lost 114 files relating to complaints about abuse between 1979 and 1999.
But the first two women appointed to chair the inquiry both resigned over concerns about their links to the establishment.
Opposition Labour lawmaker Simon Danczuk, who has campaigned on the issue, lamented the lack of progress.
"Theresa May has a once-in-a-generation opportunity to address child abuse failings of the past," he said.
"But so far all we've seen are whitewash reports and hopeless attempts to manage and contain an historic child abuse inquiry.