The Foreign Office has refuted reports that seven-year-old Julian Alessandro Cadman, who has been missing since Thursday 17 August's terrorist attack in Barcelona, was found alive and well at a local hospital.

Julian became separated from his mother Jom Cadman during the chaos of the attack, in which a van was driven into a crowd of pedestrians in Barcelona, killing 14 and injuring at least 100. Two more were killed in related attacks along the Spanish coast.

Jom remains in a serious but stable condition in hospital.

The Foreign Office has not yet named the child, believed to be a dual British-Australian national, but an appeal on Facebook from his grandfather Tony Cadman revealed his name.

"My grandson, Julian Alessandro Cadman, is missing," he wrote, sharing a photo of Julian and urging the public to share it themselves.

"We have found Jom (my daughter in law) and she is [in a] serious but stable condition in hospital. Julian is seven years old and was out with Jom when they were separated, due to the recent terrorist activity.

"Please share if you have family or friends in Barcelona."

Julian's father Andrew and other members of his family flew out to Spain to search for the boy.

In a statement the Foreign Office said: "Our thoughts are with the victims of these terrible attacks and the people of Spain. We are currently assisting a small number of British people affected and are working to find out if any more need our help. We have deployed additional staff to Barcelona and have offered support to the Spanish authorities."

The Philippines government said on 19 August that a seven-year-old missing following the attack is the son of a 43-year-old Filipino woman who was living in Australia. Foreign Affairs Undersecretary for Migrant Workers Affairs Sarah Arriola said the boy and his mother were in Barcelona to attend a wedding.

Following Tony Cadman's appeal, Prime Minister Theresa May said that the Foreign Office was "urgently looking into reports" that a child was missing. She did not name the boy. Australian prime minister Malcolm Turnbull also made an appeal for his safe return.

"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," he said.

Two suspects were arrested and another was killed by police after the van ploughed into people on La Rambla, a pedestrianised area popular with locals and tourists. A manhunt is underway for a fourth suspect, Younes Abouyaaqoub, believed to be the man who drove the van.