UK Prime Minister Theresa May says her thoughts are with the victims of the “terrible attack” in Barcelona.
“The UK stands with Spain against terror,” she added.
Officials in the city say at least 13 people were killed and 80 hurt when a van ploughed into pedestrians on the main street of Las Ramblas.
The Foreign Office has issued advice to tourists to “stay inside and away from Las Ramblas” and wait for police to say it is safe to move.
It said it was in contact with local authorities.
Labour leader Jeremy Corbyn tweeted: “Terrible reports from Barcelona. My thoughts are with those killed and injured, and the emergency services working to save lives.”
Boris Johnson, the foreign secretary, also expressed his condolences on Twitter. “Concerned and saddened by #Barcelona attack. Our thoughts are with those affected. Doing all we can to identify whether Brits need help,” he wrote.
Sadiq Khan, the mayor of London which has seen two similar vehicle attacks in recent months, tweeted his thoughts were “with the victims of this barbaric terrorist attack in the great city of Barcelona”.
“London stands with Barcelona against the evil of terrorism,” he added.
Rizza Javier, from Essex, was eating with her husband at a nearby restaurant in Barcelona.
“We suddenly heard and saw people screaming, crying and running in the street, some came inside the restaurant so I grabbed my son to the upper floor of restaurant.
“A bus stopped right in front and a couple who came out of the bus saw the van, they told us there was a van who rammed into people in the street,” she said.
The family were forced to stay locked in the restaurant for two hours, she said.
“We were all scared because the van was near the restaurant and we were told the terrorist was on foot.”
Aamer Anwar, a lawyer and rector at the University of Glasgow, was walking in Las Ramblas when he heard screaming.
He said a shopkeeper told him five or six people were badly injured and described the scene as “chaos”
He said the police “seemed to be looking for someone. They were going very carefully, very cautiously, stall to stall.”
Former England striker Gary Lineker, who played for Barcelona in the 1980s, tweeted: “Deeply saddened to hear about the attack in the wonderful city of Barcelona.
“What purpose this barbarity serves is beyond comprehension.”
Manchester City manager Pep Guardiola, a former Barcelona midfielder and coach, said: “All at MCFC are saddened to hear of the attack in the City of Barcelona. Our thoughts are with all affected and the emergency services.”