Footage shows the 212 bus - full of schoolchildren - speeding around a corner moments before a horror crash that left 19 people injured.
The bus is seen to swerve as the woman jumps across to the pavement.
Tina Hogan, 58, who works at the cafe, said: “The woman came in such a fright and said that she was nearly hit.
“The bus was speeding - I’m sure of it. Some people have told me that they think the brakes were shot.
“The poor woman was shocked.”
Emergency services were called to the scene after the incident on Selwyn Avenue, in Chingford.
Witnesses say they rushed to the scene to help children off the bus.
Five casualties, including three schoolchildren, were taken to hospital while more than a dozen other passengers suffered minor injuries and were treated at the scene.
The driver of the bus had to be cut free from the vehicle before being taken to hospital.
Another have-a-go hero, who was drinking a tea in the cafe at the time, revealed he also went to go help the injured.
He said: “I was in the coffee shop and heard the crash.
“We couldn’t open the front doors they were jammed shut. We got everyone off when we could.
“We went to see the driver, he was stuck but he was conscious.
“I just stayed with the injured - there was a lot of blood from the head injuries.
“The girl was not moving initially, I thought she was dead.
“There was a strong pulse and it looked like a lot of blood was coming out from near her eye.”
Eric Garip, 38, who runs The Corner Cafe, said he rushed to the scene when he heard the bus crash about 25 metres away.
He said: “We heard a very big bang.
“I just ran to them and tried to open the back doors.
“I opened the front door, that didn’t open either until someone else tried to open it from the inside.
“There was one near the bus drive not moving at all, and another one up the stairs, the two girls were the main injured ones.
“There were around Year 7 or Year 8 kids. I then went to the bus driver and he said he couldn’t come out: ‘I’m squashed. I can’t move my foot.’
“I went back to the kid who was injured and the mum was injured. I was slowly helping them out and take them outside.
“The kids were all scared, crying panicking. The parents were panicked. I said come outside, it’s safe, and slowly all the kids and parents left the bus. A few adults came and helped as well.
“I’m just worried about the two kids in hospital. We don’t know whether they’ll be okay or not.
“The driver was okay. He was obviously panicked and shocked.”
Phil Grundy, headteacher at Highams Park School, said last night that the two pupils, which were taken to hospital, are expected to be discharged today.
“II would like to reassure you that the two students from Highams Park School who were taken to hospital have received excellent treatment and are in good health considering the seriousness of the accident,” he said.
“They both hope to be discharged later this evening or tomorrow.
“All other Highams Park students that were hurt have received medical care at the local medical centre and many students involved have received counselling and pastoral support during the school day.
“Our thoughts and concern are also extended to a student from another school who also required hospital treatment as well as the numerous members of the public who were injured on the bus.”