The woman was walking with a 10-month-old baby girl and a dog when she was struck by a car while on the pavement of Church Avenue yesterday afternoon.
She has not been named but it is understood that she is the child's grandmother.
An air ambulance landed at nearby Horsforth School and medics battled to save her at the scene. The baby escaped with minor cuts.
Andy Sykes, who lives on nearby Long Row, said he had written to local MP Stuart Andrew in the past to raise concerns about the road.
"It is a very busy road. Me and my wife have written to Stuart Andrew asking for speed bumps to be installed. It is very difficult to cross safely, because of the volume and speed of the traffic," said the 35-year-old, a lecturer in animation at the University of Leeds.
"It was a horrible shock. It must be devastating for the family. We spend last night in a state of shock. You don't expect something like this to happen outside your front door."
Roofer Martin Wilson, 50, was working on a house about 100 metres from the scene when the accident happened.
"I heard a loud bang. I looked over and saw the car stop. A man got out and went straight to the pushchair on the road. He picked up the baby and gave it to a woman. He then went over to the (injured) woman, who was laid in the road.
"It was mayhem. People came out of the fish shop to help. I think the dog had been tied to the pushchair, and some people released it."
Young mum Caroline O'Shaugnessy, 38, whose son is nine months old, said neighbours feared she had been the victim of the collision.
"I saw a bag of shopping and an elderly couple holding the baby. The pram was damaged. The lady was lying in the road and people were around her. Me and the couple made sure the baby was OK - she had grazes on her hand. She was crying a little.
"People go so fast on that road and navigate the bend too fast. As a lady with a pram myself, it's a massive worry. A neighbour called round last night because she was worried I had been involved in the accident.
"I am planning to write to the MP and ask for traffic calming measures or a one-way system. Something needs to be done."
The driver of the car has been arrested.