Winnie was left with a puncture wound to her leg and Emma, 38, was also injured when the dog jumped up at her.
Emma said police were dragging their feet in their response to the attack.
“I phoned 101. They told me to speak to crime management. They then basically told me they have a high numbers of crime in the area at the moment so there would be a delay, and then passed me on to Richmond Safer Neighbourhoods,” Emma said.
“I’m sharing this because I feel no one is listening and the community is at real risk. Does a toddler need to be serious injured before proper action is taken?”
Footage shows Emma had to lift Winnie to safety after the other dog slipped out of its owner’s grasp to attack.
Emma and Winnie then sought refuge in the fishmongers.
Emma said: “If I had not whipped Winnie in the air I think the dog would have killed her. I’m the mum of a two-year-old and was on my way to pick up my daughter, if I had her with me I just couldn’t have done what I did.”
A Met Police spokesperson said: “At 5.55pm on Monday, September 1, police received a report of a dog attack in Twickenham. A dog and its owner, a woman in her 30s, were injured in the incident.
“It is believed the woman suffered scratches and the dog a puncture wound.
“An emergency response team attended the scene to carry out enquiries and take statements. The case was assigned to a neighbourhood officer for further investigation who has made contact with the victim today, Wednesday, 3 September.
“The suspect dog and its owner made off before police arrival. Enquiries are ongoing about what breed the dog was.
“Anyone with information is encouraged to contact the Met via 101, quoting 01/7922862/25.”
Winnie required anti-biotics after the attack, vets notes state that a “bully-like dog” attacked her back end/tail but that “luckily she was saved before much damage could occur”.
Winnie has been anxious since the attack but is taking some quiet time to recover, Emma said.