Julian's mother, Jom Cadman, is in hospital as she recovers from her injuries.
His mother has been traced and is said to be in a serious but stable condition in hospital.
Another Sydney woman, Suria Intan, on the last few days of a European holiday with friends is also in a serious condition in hospital.
The grandmother of missing British boy Julian Cadman says she is "worried sick" as she waits for news about the seven-year-old.
It was still not clear how many people had been involved in the van attack and other incidents on Thursday.
British Prime Minister Theresa May said the United Kingdom is urgently looking into reports a child with dual nationality, believed to be Julian, is missing, the BBC reports.
Australia has said one of its citizens is unaccounted for, and three were injured, without providing further details.
"All of us as parents know the anguish his father is going through and his whole family is going through, as they rush to seek to find him in Barcelona".
Injured are helped after the attack.
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Her brother, Will has also paid tribute to his sister's resilience on Facebook with a picture of her recovering in hospital. She said she spent the last four weeks trying to navigate her way out of the woods but ended up going around in circles.
Speaking after Julian's grandfather made a plea for information, Theresa May said United Kingdom authorities were "urgently looking into reports" that a child, who has dual British nationality, is missing.
It is understood two men from Victoria were hit by the auto and injured, and both have since been discharged from hospital.
A 3-year-old Spanish boy and his mom were among the 13 killed when a terrorist van slammed into pedestrians in Barcelona, according to reports Friday.
Julian was born in Britain, but moved to Australia when he was three, the newspaper reports.
"Our thoughts are with the victims of these awful attacks and the people of Spain", a spokesperson said.
Sadiq Khan said London stood with Barcelona "against the evil of terrorism" following recent attacks in Westminster, London Bridge and Finsbury Park.
The dead, the missing and the injured from the deadly terrorist attack Thursday came from dozens of countries in Europe, Asia and the Americas to spend time in Las Ramblas, one of the most joyous, vibrant streets in Europe, only to be mowed down by a white van.
"He turned up to work this morning, turned the news on this morning at 6 o'clock, heard about it, tried to ring his Mrs, couldn't get hold of her", he said.
An Italian man, 35-year-old Bruno Gulotta, a father of two, was the first victim to be named.