Sir Denis O'Connor, outgoing HM Chief Inspector of Constabulary, will give evidence on Olympics security.
Stephen Greenhalgh, Deputy Mayor of London for Policing and Crime, will give evidence on policing in London.
Metropolitan Police Commissioner Bernard Hogan-Howe has also been asked to give oral evidence.
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Marjorie and Michael Cawdery, both 83, are understood to have been stabbed to death in a killing their family called "incomprehensible".
Detectives have launched a murder investigation following the shooting in Brent, north west London on Friday night.
Hot and humid throughout the Bank Holiday Weekend.