Sir Bernard Hogan Howe said reports of "lorry loads" of shredding did not match up with the accounts he had heard.
In terms of when we knew about the shredding, it was on February 4 this year when officers who were providing information to Mr Ellison became aware by talking to a witness that there had been some shredding and immediately - or by the fifth - we shared that information with Mr Ellison.
The Home Affairs Select Committee will today take evidence on the Stephen Lawrence Independent Review from Metropolitan Police Commissioner Sir Bernard Hogan-Howe.
He is expected to answer questions on alleged corruption in the Force during the Lawrence murder inquiry.
Mark Ellison QC uncovered possible evidence of corruption in Met Police during his review of the Lawrence murder investigation. Stephen Lawrence was murdered in South East London in 1993 and the Metropolitan Police have been heavily criticized for their handling of the case.
One of Britain's top officers took part in a series of dawn raids during a drugs crackdown across the capital today.
Metropolitan Police Commissioner Sir Bernard Hogan-Howe joined Operation Hawk, which involves stamping out drug dealers in London.
More than 500 drugs warrants were executed by hundreds of officers as part of Operation Hawk, in a crackdown on street-level drug dealing in 32 London boroughs.
The force also launched a "mock cannabis farm" inside an old police command vehicle, which will be shown to communities across London to help raise awareness.
The mock cannabis farm is complete with equipment recovered from farms, including fans, lights, cables and other paraphernalia. Officers will be on hand to explain the dangers of growing cannabis.
Commander Stephen Watson, who led today's raids said: "Drug dealing and cannabis cultivation damage communities and generate organised and violent crime, money laundering and anti-social behaviour.
"The MPS is determined to tackle this issue head on with the assistance of London's communities, many of whom cite tackling drugs as a priority for local safer neighbourhoods teams.
"While activity to tackle drug dealing has always been a high priority for the MPS, with major operations carried out with partners against high-level drug dealers on a regular basis, Operation Hawk's focus is to increase operational activity on drug dealing at neighbourhood level."