The 31-year-old woman and her daughters, aged eight and three, were attacked in Lessar Avenue at 7.25pm on January 31.
They were taken to hospital following the incident in which a man threw a corrosive alkaline substance at them.
In an update issued by the Metropolitan Police Commander Jon Savell, he said the mum remains very poorly in hospital and is sedated.
He added that it was likely she had suffered life-changing injuries as a result of the incident.
The injuries of the two children are not as serious as first feared, and it is believed they will not be life-changing.
Police are continuing to search for Abdul Shokoor Ezedi, who is from Newcastle, in connection with the attack.
The 35-year-old suspect is described as having very “significant injuries to the right side of his face”.
Abdul Ezedi was last seen at King’s Cross Underground Station at 9pm on Wednesday.
A total of five search warrants were carried out overnight, including at two addresses in east London and three in Newcastle.
Two empty containers with corrosive warnings on the label were found at an address in Newcastle.
Forensic tests are currently ongoing to see if the containers held the substance used in the attack in Clapham.
Commander Savell said: “Following the attack, we know he travelled from Clapham South Underground Station to King’s Cross Underground Station and I want to appeal for anyone who may have seen him travelling on this route between 7.30pm and 8pm.
“The latest confirmed sighting of the suspect is at exactly 9pm, when he is seen boarding an underground tube at Kings Cross station on the Victoria line southbound.
“As you have seen from the image we have released of Abdul Ezedi, he has suffered a serious facial injury.
“I’m making a direct appeal – hand yourself into police, not only so we can speak to you, but so you can get the urgent medical treatment you obviously need.
“Any members of the public with any information about the attack or the whereabouts of Abdul Ezedi are asked to call 020 7175 2784.
“I also ask anyone with any video footage, including video doorbell or dashboard cameras to please contact us immediately.
“I would also like to reiterate the fact that if you see Ezedi, call 999 immediately. He should NOT be approached.”
Three women – two in their 30s and one in her 50s – who were injured when they bravely came to the aid of the family, have all been discharged from hospital with minor burns injuries.
A man in his 50s who also helped declined hospital treatment for minor injuries he suffered.
Five officers who were injured as they responded have all been treated and have left hospital.
Here is a full timeline of Ezedi’s movements on January 31.
- 12.15am – Ezedi’s vehicle is seen in Newcastle
- 6.30am – His vehicle is then seen traveling into Tooting, London
- 4.30pm – A further sighting of his vehicle is confirmed in Croydon
- 7pm – He is then seen driving in Streatham
- 7.25pm – Attack takes place in Lessar Avenue, SW4, before Ezedi makes off in his vehicle which crashes nearby. He leaves the car and runs off.
- 7.33pm – Ezedi boards a train at Clapham South Tube Station.
- 7.59pm – He is then seen leaving that train at King’s Cross Tube Station.
- 8.42pm – He is then seen on CCTV leaving Tesco at 21 Caledonian Rd, London N1 9DX. He exits and turns right.
- 9pm – Ezedi enters King’s Cross Tube Station and boards a Victoria Line tube Southbound.