The woman remains in a critical condition in hospital and may lose the sight in her right eye, police said on Monday. She has so far been unable to talk to officers because she is too unwell.
In a new update on Monday, detectives said they had spent hundreds of hours looking for the fugitive, who they described as a dangerous offender, but warned the search could take weeks. He was last seen near Southwark Bridge, which crosses the Thames, but there is no suggestion that he jumped into the river.
Commander Jon Savell said investigators are keeping an open mind as to where he may be or what may have happened to him, but suggested he could have come to harm or that somewhere is protecting him.
They added that Ezedi is not the father of the children injured in the attack but was believed to be in the capital visiting the victim. They still do not yet know why he carried out the attack.
During the media briefing at New Scotland Yard, Commander Jon Savell said: "Our manhunt continues at a considerable pace we have hundreds of specialist detectives working on this.
"We are taking it incredibly seriously.”
Describing the woman’s injuries, he said: “He is very dangerous offender who has caused some horrendous injuries to a mother.
“The mother remains sedated. She is very critical but stable. She had very significant facial injuries that undoubtedly will be there for the rest of her life unfortunately."
He warned that anyone hiding Ezedi that it is a criminal offence, adding: "We will take action".
The most recent sighting of Ezedi, who is from Newcastle, was at about 9.50pm on Wednesday, near the bridge in south London.
Officers said they had arrested a man, who was questionned in a south London police station and later bailed.
Police, including counter-terror officers, have scoured hundreds of hours of CCTV. Officers revealed he was using a bank card to travel the tube network but that card has not been used since Wednesday.
They have recovered the suspect’s vehicle from the crime scene which has been difficult to examine because of the dangerous corrosive substance found within the vehicle. They believe they have it narrowed down to one or two very strong Alkalines.
Forensics have also recovered his mobile phone which has helped understand how suspect and victim knew each other.
But the fact that the suspect does not have a phone makes the manhunt more difficult, they added.
Commander Savell added: "He may have come to some harm is obviously one hypothesis. It’s realistic to understand the fact that no-one has seen him recently, he’s not been spotted by anybody would mean he has either come to harm and he’s lying somewhere yet to be found.
“Or someone’s looking after him and he’s not been outside in some time. That are the obvious two hypotheses.
"We haven’t ruled either out but our main focus is to try and find him alive."
Asked by The Independent if they have begun searching the River Thames, Det Supt Rick Sewart said: "Not at this stage but we are continuing our inquiries in that particular area so that we can understand more about where he went next.
"If we have any information to suggest he may be in the Thames then we will move to that line of inquiry."
Police have offered a £20,000 reward in place for anyone with information leading to Ezedi’s arrest.
More than 200 calls have been received from members of the public with potential sightings, but they have since been discounted.