A video of the incident, which saw the Great Britain sprinter and her partner, Ricardo dos Santos, pulled from their car in a London street, was posted online by former Olympic medallist Linford Christie.
Williams has said she believes officers racially profiled her and dos Santos – a Portuguese 400-metre runner – when they were handcuffed and separated from their three-month-old son.
The Met has voluntarily referred itself to the police watchdog, despite two reviews by the force’s directorate of professional standards finding no misconduct by its officers.
Dame Cressida told the Home Affairs Select Committee on Wednesday: “We apologised yesterday to Ms Williams and I apologise again for the distress this stop clearly caused her.”
The commissioner said reviews of the evidence by two separate teams have found there was no apparent misconduct, but explained a referral was made to the Independent Office for Police Conduct (IOPC) because of “the level of public concern”.
She said: “Yesterday two of my officers spoke on our behalf to Ms Williams, and I think all of us watching could empathise with somebody who is stopped in a vehicle, who has a young child in the back, who does not probably know what exactly is going on, and is subsequently found, together with her partner, not to be carrying anything illicit.”
Dame Cressida said she has asked a senior officer to review the Met’s handcuffing practices to make sure it hasn’t become a “default”, and has set up an “oversight group” looking at the use of force.
“Every time we see a video that is of concern we review them, we see if there are any lessons learned,” she told MPs.
“My senior officer has said… I’m sorry to Ms Williams for the distress, it has clearly caused her, and I say that, too.
“So, if there are lessons to be learned from it, we will learn them, and I’m looking at handcuffing as a specific issue.”
Nothing was found in the search, which the Met said was carried out by officers patrolling the area in response to an increase in violence involving weapons.
The force also said the vehicle was seen driving suspiciously, including on the wrong side of the road, and that the driver sped off when asked to stop.
But this account was rejected by Ms Williams, who has said she is considering legal action against the Met.
IOPC regional director Sal Naseem said the watchdog will be looking at whether the use of stop and search was “appropriate and proportionate”.
He added: “We will also investigate if racial profiling or discrimination played a part.”