Lord Blair told the House of Lords there were "widespread concerns" over the Met's actions and said: "I share some of them."
He called for a report on the issue to be published "as soon as possible".
The Met said his views could be considered as part of a report.
Lord Blair said he believed the current Met Commissioner, Sir Bernard Hogan-Howe, recognised there had been shortcomings.
This had been shown by Sir Bernard's apology to some of those affected, and his decision to appoint retired judge Sir Richard Henriques to "enquire into his force's conduct", Lord Blair added.
A spokesman for the Met said: "The commissioner has publicly expressed a view that suspects should have anonymity until charged which would be the best way to deal with this issue, but Sir Richard Henriques can consider Lord Blair's views as part of his report if he wishes."
Another former senior Met officer, Lord Paddick, criticised the force's investigation into DJ Paul Gambaccini, who spent 12 months on bail before being told he would face no charges.
"It must have been apparent very quickly that the allegations were never going to be substantiated," he said.
And he questioned whether some high-profile investigations had been "deliberately protracted to give the impression that the allegations are being taken seriously".
A former Metropolitan Police commissioner has criticised the way the force dealt with historical child sex abuse allegations against politicians and celebrities.