Officers arrested and interviewed the man on Monday and have since released him on bail while detectives also issued new images showing him in Allhallows Lane, near Monument and leading to the Thames at 9.47pm on Wednesday.
He was also seen on Southwark Bridge in London on Wednesday at about 9.50pm, several hours after he is suspected of dousing a mother and her two children with a corrosive substance.
Detectives are working on the premise that he is either being hidden by someone or has come to harm.
He was using his bank card to travel around on the Tube network, but the card has not been used since Wednesday.
Ezedi does not have his phone on him - which makes the search more challenging, officers said. The phone has been recovered and analysed by police.
Ezedi, 35, bought 30 eggs in a convenience store while smiling at the shop worker on the till.
The images were caught near to his home on Tuesday before he travelled to south-west London ahead of the attack that took place at around 7.25pm on Wednesday evening.
He was found guilty of sexual assault in 2018 but granted asylum after claiming to have converted to Christianity.
However, staff at the shop told the Telegraph they were 'horrified' that Ezedi had been connected to the attack because he was known as a 'good Muslim'.
A £20,000 reward has been offered as part of the manhunt for Ezedi, who suffered a serious injury to the right side of his face.
He is suspected of hurling an alkaline substance at the 31-year-old woman and her daughters aged eight and three, on Wednesday evening.
The woman may lose the sight in her right eye after the attack, while her daughters, who were also hurt but have since been discharged from hospital.
Investigators are trawling through hundreds of hours of CCTV and have tracked Ezedi’s movements on the Tube network via his bank card, with the latest sighting now on Southwark Bridge at 9.50pm on Wednesday.
An NHS worker who witnessed the attack described how the three-year-old was thrown like a "rag doll" to the ground by the attacker.
Ezedi tried to drive off after the attack but crashed and instead fled on foot.
He boarded a Northern line train at Clapham South Tube station at just before 7.35pm.
The got off at King’s Cross just before 8pm. He was the captured on CCTV leaving a Tesco Express on Caledonian Road, near King’s Cross. He entered King’s Cross Tube station at 9pm and boarded a southbound Victoria line train.
He was then seen on CCTV leaving Tower Hill underground station and going to to Southwark Bridge and Allhallow's Lane.
Police have said that they will issue footage from a further sighting on Southwark Bridge but since that the the trail has gone cold.
Nick Aldworth, a former national counter-terrorism co-ordinator, suggested Ezedi, from Newcastle, could have taken his own life or be using an ally as there had been no further sightings since he exited at Tower Hill Tube station in east London at 9.16pm on Wednesday, shortly after the attack.
He told BBC Radio 4’s Today programme: “I think if we’ve not seen or heard from him in the last couple of days, which appears to be the case, he’s gone to ground, possibly supported by somebody… or it’s not unlikely or improbable that he may have taken his own life. There is therefore a body to be found somewhere.
“The reason they’ve offered a £20,000 reward is usually because there’s a sense that somebody inside the community might well be harbouring this individual."