The incident occurred shortly before 7.30pm on Wednesday, 23 July at Goodge Street Station.
Chief Inspector Mark Lawrie said: "This was a frightening incident, not just for the scale of the danger the child was exposed to, but also because the woman then put her own life on the line by going onto the tracks.
"We urgently need to identify the people involved to ensure the child wasn't injured as a result of the fall onto the tracks.
"I have taken the step of releasing CCTV of the people involved to highlight the very real concern we have for all involved."
Chief Insp Lawrie said the incident showed how "when used incorrectly [the rail network is] a hazardous environment, and the proper care should always be taken".
Phil Hufton, the chief operating officer for London Underground, said: "London Underground has an excellent and continually improving safety record and such incidents on the Tube are very rare.
"The safety of our customers is our number one priority and like on all railways we advise customers to take care when travelling on the network. I urge anyone who knows the family involved to contact British Transport Police."
Police said they wanted to contact the people involved in the incident to check they were not injured, and urged anyone who recognised them or has any information to get in touch.
- UK Independent