Reports have emerged suggesting that Driss Oukabir had handed himself into police after seeing his photograph being circulated online and in the media.
He apparently told officers that his identification documents had been stolen before the attack and that he had played no part in it.
There is no official confirmation on this from the authorities, however.
Theresa May has released a longer statement, saying the Foreign Office is in close contact with the authorities in Spain.
I am sickened by the senseless loss of life in Barcelona today.
The Foreign Office is working to establish if any British nationals were involved in this appalling incident and we are in close contact with the authorities in Spain, who have our full support.
Following the attacks in Manchester and London, Spain stood alongside the British people. Tonight, Britain stands with Spain against the evil of terrorism.
Carles Puigdemont, the Catalan president, has declared three days of mourning for the region. He said:
Catalonia has been, and will be, a land of peace. A place of welcome. And we will not let a minority end our way of being that has been forged over centuries.
Tomorrow at noon people will gather in Plaça de Catalunya for a minute’s silence.
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My colleague, Sam Jones, has this on the only named suspect:
Within hours of the attack in Barcelona, Spanish police had begun investigating Driss Oukabir, a 28-year-old man who was born in Morocco. He is thought to be the first person arrested in connection with the atrocity.
Reports suggested that Oukabir hired the white Fiat van used in the attack from a rental company in a town around 25km (15 miles) from the centre of Barcelona.
According to Oukabir’s Facebook page, which was later taken down, he had lived in the French city of Marseilles but moved to the Catalonian town of Ripoll. Police sources said that he has a NIE – the identity card issued to foreigners who live in Spain.
The Spanish newspaper ABC reported that although a warrant had been issued for his arrest over allegations of domestic abuse, police did not suspect him of any jihadi activity. El País said he had spent time in prison in Figueres, Catalonia, and had been released in 2012.
The number of those seriously injured in the van attack has risen to 15, according to Catalonian police. The Press Association is reporting that more than 80 people have been injured. The total number of fatalities remains at 13.
Prominent lawyer and University of Glasgow rector Aamer Anwar was walking in Las Ramblas when he heard a crashing noise followed by screaming.
He said the police were very quickly on the scene following the attack.
Anwar said:
I had been to the cathedral and was walking down Las Ramblas for something to eat. Part of it was in the shade so I decided to keep walking down and literally within 10 seconds there was a crashing noise. I turned around and people were screaming. I could see a woman screaming with her kids. People started running and jumping into shops. I ran for about 50 or 100 metres and stopped to see what was happening.
The police were very quickly on the scene and getting people to move back. I could see chaos right at the top area and I spoke to a shopkeeper who had run down and was screaming. He was Bengali so I spoke to him in Urdu and he said a van had driven into a crowd and he thought there were five to six people very seriously injured.
[The police] seemed to be looking for someone. They were going very carefully, very cautiously, stall to stall.
Islamic State has claimed responsibility for the Barcelona attack, the group’s Amaq propaganda news agency said.
“The perpetrators of the Barcelona attack are soldiers of the Islamic State and carried out the operation in response to calls for targeting coalition states,” the agency said, referring to a United States-led coalition against the Sunni militant group.
Isis claims of responsibility are unreliable, and do not necessarily indicate a direct connection between the attacker or attackers and the terror group.