John Dickinson, one of the lawyers representing the Iraqis in the al-Sweady case, said the inquiry has taken so long to set up, because it was "vigorously opposed" by the MOD.
More than three years after it was ordered, the inquiry will examine claims that UK soldiers murdered 20 or more Iraqis, and tortured detainees in Maysan Province, southern Iraq, in May 2004.
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At least 27 high-rise blocks of flats in 15 local authority areas have failed fire cladding safety tests, the Government has announced.
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The company said its role was not to decide what was or was not compliant with local building regulations.