While recorded crime fell 2% in the quarterly figures, the alternative British Crime Survey (BCS), which polls people's experience of crime, found overall offences in England and Wales fell 5% in the 12 months to June 2005.
During the same period, 24% of people were the victims of at least one crime, the BCS indicates - the lowest percentage since the survey began in 1981.
Mr Clarke said: "This is a considerable achievement demonstrating the success of government initiatives on crime reduction and should not be underestimated.
"However, I recognise that the fear of crime is too high - it is not enough to reduce crime if people do not perceive that reduction.
Shadow home affairs minister Edward Garnier said violent crime was continuing to "spiral out of control".
He said: "The government should defer 24-hour drinking until it has got a grip on the problem of binge-drinking, which is fuelling violent crime."
Mr Garnier also blamed "the government's failure even to begin fighting the war on drugs" for rising violence.
New licensing laws allowing 24-hour drinking are due to come into force on 24 November.
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