Though he does imply that intelligence services engineered the attacks using the 4 alleged bombers as 'patsies'.
In any case it's more likely to be MI6 than MI5 since the formr work very closely with foreign intelligence agencies such as the CIA and Mossad who love to have free rein to operate here in the UK and are quite literally 'above the law' as they operate outside the jurisdiction of British law they don't have to obey it, hence the 'Licence to Kill'.
Likely that this was an MI6 operation and that MI5 had been kept out of the loop or otherwise warned off as a result.
Consider also that the head of MI6, John Scarlett, is a war criminal who helped prepare the 'dodgy dossier' lies that led to the illegal invasion of Iraq.