Eleven people, including a young family, needed hospital treatment after an attack using a corrosive alkali substance.
A mother and her three-year-old daughter were the most seriously hurt, with potentially life-changing injures.
Police believe they and her second daughter, aged eight, were the targets of the attack in Clapham, south London, after which five police and three passers-by also needed hospital treatment.
London’s Metropolitan Police said the mother, 31, and both daughters, remain in hospital.
The suspect has been identified as Abdul Ezedi, 35, from the Newcastle area in north-east England
Police say he is “dangerous”, and that they believe he knows the mother.
The attacker crashed his vehicle into a stationary car as he tried to escape before fleeing on foot, police said.
Three members of the public who came to the aid of the family – two in their 30s and one in her 50s – have been discharged from hospital with minor burns injuries. Five police officers also needed treatment.
"I heard a bang and I heard someone saying ‘help',” said bus driver Shannon Christi. "I run outside and as I run outside I've seen this guy throwing a child on the floor, he picked her up and threw her again.
"So, at that point I ran in and I grabbed her and took her into my block."
Ms Christi said both girls were crying.
"I've then seen her mum walking up the road again saying 'I can't see, I can't see'," she said. "(We were) dousing her in water. Staff from the hotel came around and asked what's going on and I said she needs water."
She described the mother as Asian.
Superintendent Gabriel Cameron, a senior officer in Lambeth: "Officers from across the Met are working with partner agencies and forces to locate and arrest the man. While this appears a targeted attack, he is a dangerous individual and we urgently need to find him.
He also praised the members of the public who came to the aid of the family injured in the attack.
Supt Cameron said: "All these members of the public and my officers deserve enormous recognition and praise for coming to the aid of this woman and children in what must have been a terrifying scenario."
Metropolitan Police Commissioner Mark Rowley said: "Fortunately, attacks using acid and chemicals are exceedingly rare. We did have a spate of them two or three years ago. It's not something we've seen much of at all recently, I'm pleased to say."
