The athlete accused the force of “racially profiling” her, and her partner, Ricardo dos Santos, when they were handcuffed and separated from their three-month-old son.
The three police officers are now subject to a gross misconduct investigation over “potential breaches of police standards of professional behaviour”, the Independent Office for Police Conduct (IOPC) has said.
Three other police officers are also being investigated over the incident last July.
Commissioner Dame Cressida Dick has previously apologised to the athlete after footage of their car being stopped in Maida Vale, West London, was posted online by the former Olympic medallist, Linford Christie.
An IOPC spokesperson said: “Three MPS officers are now subject to a gross misconduct investigation for potential breaches of police standards of professional behaviour.
“The three officers were already subject to a misconduct investigation for various potential breaches of police standards of professional behaviour relating to the use of force; duties and responsibilities; and authority, respect and courtesy.
“After reviewing a range of new evidence, they were informed they are now subject to an investigation for potential breaches of the police standards of professional behaviour relating to equality and diversity, which requires officers to act with fairness and impartiality and not to discriminate unlawfully or unfairly.
“Two of those officers are also now being investigated for potential breaches of the standards relating to honesty and integrity, requiring them to be honest and act with integrity at all times.
“Collectively, these alleged breaches amount to potential gross misconduct.”
It said a fourth officer is being investigated for potential breaches of the standards relating to “equality and diversity, and duties and responsibilities”.
Two other officers also face an inquiry over behaviour relating to use of “force; duties and responsibilities; and authority, respect and courtesy”.
It added: “Our investigatory work has now concluded and preparation of the final report is under way.”
Earlier this year, it was announced a review would take place into the use of handcuffs where an arrest has not been made – a tactic most commonly used during stop and search.
Ms Williams welcomed that announcement, but said further “effective” racial bias training was also needed.
The sprinter said: “The handcuffs were painful and it was incredibly humiliating to be separated from my baby, in handcuffs outside my home with neighbours walking past.
“While I welcome better training in the Met on the use of handcuffs, the trauma of the incident did not start or end with the handcuffing. It was racial stereotyping and prejudice.
“I would like to see some effective bias training in the police as well as better training on the use of force and not just in relation to handcuffs.”