The investigation followed a referral from the Metropolitan police in November 2011 after it identified failings in its original investigation into the assault.
Recent snap inspections of some Birmingham schools as part of the so-called Trojan horse affair identified failings to safeguard pupils from extremism – an observation that had not been made in previous inspections.
The MoD said an internal board of inquiry in 2004 had "similarly identified failings that contributed to this incident and made 12 recommendations, all of which were accepted and have since been implemented".
Sir Brian's comments come after the publication of the highly critical Francis report into poor care at Stafford Hospital which identified "failings" across the NHS and recommended reforms of the health system.
The report also identified failings in oversight by the DfE as well as the council and Ofsted, saying: "It is not possible to discern a relationship between Birmingham city council (BCC), Ofsted, the DfE and the Education Funding Agency in the process of sharing critical data and intelligence".
McAvoy said government agencies and other individuals and bodies had already been issued with notices to produce evidence, while Callaghan noted that at least a dozen previous reports had identified failings in the system which would be examined by the commission.
"The overriding objectives of the review are to ensure that any possible failings by the FA and clubs at the relevant time are brought to light and to ensure that lessons are learned so any identified failings are not repeated," the FA said in a statement.
The public inquiry into the poor care at Stafford Hospital, published in February, identified failings in the way hospitals are monitored.
