A study by Mr. Julian Roberts commissioned by the Department of Justice prior to the imposition of minimum penalties came to the same conclusions as you have. This study looked at all Commonwealth countries.
As you all know, in 2005, the legislation was amended to include several minimum penalties for sexual offences against children. The current legislation also provides for increases in the minimum penalties agreed to in 2005.
Are you aware of any studies that came to the conclusion that the minimum penalties imposed in 2005 have achieved the desired results?