Williams had been in the West London neighborhood of Maida Vale with her partner, Portuguese 400 meter record holder Ricardo dos Santos, and their three-month-old son when they were stopped by police last weekend.
On Twitter, Williams said she welcomes the referral of Saturday's "traumatic" incident to the Independent Office for Police Conduct as a complaint and that "the IOPC has said that their investigation will also look at what part racial profiling or discrimination played in the incident."
An independent investigation is now "necessary", says Williams, "as the Metropolitan Police have proved that they cannot be trusted to investigate a complaint themselves, having already publicly stated that there has been no misconduct.
"They published these findings on Twitter before taking a single step to formally record or investigate why their actions caused our family so much distress."
Handcuffing procedures
Williams said in the statement that she and her partner had received an apology from the police but "not for the wholly unjustified actions that officers took against our family."
She added: "We are now contacting the IOPC through our lawyers and will assist fully with the investigation, which we hope will be rigorous."
On Wednesday, the Metropolitan Police apologized to the couple for "distress caused," though the organization did not apologize for the traffic stop itself.
Police Commissioner Cressida Dick has said the Metropolitan Police will undergo a review of its handcuffing procedures after officers handcuffed Williams and her partner.
A senior official has been tasked to conduct the review after the incident, Dick told lawmakers on Wednesday.
"I don't want, and I don't believe I do, run a police service in which handcuffing is routine. It must always be justified and the justification must be in the law and written down," she said.
"Having seen a number of issues raised over the last several weeks I have said to one of my senior officers: 'Can you please review our handcuffing practices to make sure that it hasn't become in any way a default in certain situations because it shouldn't do.'"
The review will examine figures on stop and searches carried out by London's police.
"I've also got a new use of force oversight group, which involves members of the community and they'll be looking ... at these specific instances as well as data," said Dick, who offered her own apology to Williams and her partner.
"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 learnt from it, we will learn them and I'm looking at handcuffing as a specific issue."
'Racial profiing'
British Athletics told CNN: "We are aware of the hugely distressing footage of Bianca Williams and her partner being handcuffed by the police outside their home at the weekend. Our staff have been in touch with her and will be on hand for any support required.
