"And suddenly, because of that, the unforgiving nature of the military timetable, we found ourselves scrabbling for the smoking gun, which was another way of saying 'it's not that Saddam has to prove that he's innocent, we've now bloody well got to try and prove that he's guilty'."
"And we - the Americans, the British - have never really recovered from that because of course there was no smoking gun," he said.
The five-member panel also heard that Condoleeza Rice, former US secretary of state, had raised the issue of Iraq hours after the September 11, 2001, attacks.
"She said there's no doubt this was an al-Qaeda operation, we are just looking to see if there could possibly be any connection with Saddam Hussein," Meyer said.
Asked at what point war with Iraq was inevitable, Meyer said "that is a damn hard question to answer".
"What was inevitable was that the Americans were going to bust a gut to carry out the mandated policy of regime change," he said.
'Signed in blood'
Meyer also said Tony Blair, Britain's prime minister at the time, may have supported US calls for regime change after meeting George Bush, the then US president, at his Texas ranch in 2002.
He said Blair's line on Iraq seemed to harden following talks at the Crawford ranch, many of which were held in private.
Meyer told the inquiry he was "not entirely clear what degree of convergence was, if you like, signed in blood at the Crawford ranch."
The inquiry is billed to be the most wide-ranging investigation into the conflict, looking at Britain's role in Iraq between 2001 and 2009, when nearly all its troops withdrew.
On Wednesday the panel heard from a former senior civil servant who said Britain knew in the days leading up to the Iraq war that Saddam Hussein's forces may not have had the capability to deploy chemical weapons.
William Ehrman, the then director of international security for the UK foreign office, said that British intelligence was told Iraqi weapons may not have been assembled in the build-up to the conflict.
The inquiry also learnt that Libya and Iran were Britain's main security concerns before the invasion of Iraq.
The hearings are expected to climax when Blair takes the stand next year.
The Iraq inquiry will report by the end of 2010.