In July 2005, four suicide bombers detonated bombs on London's transport network, killing 52 commuters and injuring hundreds more.
Video messages left by the attackers referred to Britain's role in Iraq.
'No link to 9/11'
Manningham-Buller told the five-member inquiry panel, appointed by Britain's government, that the decision to invade Iraq had also likely provided an impetus to al-Qaeda.
"Arguably we gave Osama bin Laden his Iraqi jihad, so that he was able to move into Iraq in a way that he was not before," she said.
By contrast, the former MI5 chief told the inquiry, Iraq had posed little threat to Britain in the years leading up to the war.
"We did not believe they had the capacity to do much in the UK," she said.
She added that there was a lack of evidence linking Saddam Hussein, the former Iraqi leader, to the September 11 attacks in the US.
"There was no credible intelligence to suggest that connection and that was the judgement, I might say, of the CIA," she told the inquiry.
"It was not a judgment that found favor with some parts of the American machine.''
"It is why Donald Rumsfeld started an alternative intelligence unit in the Pentagon to seek an alternative judgment," Manningham-Buller, who was a frequent visitor to the US, said.
The inquiry, chaired by former civil servant John Chilcot, was set up last year by Brown to learn lessons from the war.
Previous probes have cleared the government of any wrongdoing.
Former UN weapons inspector Hans Blix is expected to appear before the inquiry in the coming weeks.
The inquiry is expected to conclude at the end of this year, but will not apportion blame or assign criminal liability for mistakes made.