Theresa May has pledged solidarity with Sweden in the wake of the “terrible attack” which killed four people and injured more than a dozen.
The man suspected to have been driving a lorry which mowed down pedestrians in the heart of Stockholm has been arrested, police said.
He is being questioned on suspicion of “terrorist crimes through murder” following Friday’s rampage in a busy shopping district in the Swedish capital.
A Downing Street spokeswoman said: “The Prime Minister called Prime Minister Lofven of Sweden today, to express her condolences and those of the British people for the terrible attack that took place in Stockholm yesterday.
“She was clear that the UK stands firmly by Sweden’s side, and they agreed on the importance of working together to tackle these threats, which we all continue to face.”
Ten of the 15 victims injured in the attack are still being treated in hospital, officials said on Saturday, four of whom are in a serious condition.
Two of those four are in intensive care. One child was injured but not seriously, a spokeswoman for Stockholm County Council confirmed.
Police spokesman Lars Bystrom said the man arrested is “likely” to have been the driver, but would not comment on reports in the Swedish media that he is a 39-year-old from Uzbekistan.
Mr Bystrom said only one person had been arrested in the case.
Deputy chief prosecutor Hans Ihrman approved the questioning over terror offences in the early hours of Saturday.
Sweden’s prime minister, Stefan Lofven, said: “Everything indicates that this is a terrorist attack” and later vowed he would not give in to attempts to destroy democracy.
The prime minister said: “If it is a terrorist attack, and regardless of whether it was carried out by an organisation or a lone perpetrator, the aim of terrorism is to undermine democracy, to sow discord between people so that more people will begin to hate and distrust one another.
“But those kinds of acts will never succeed in Sweden. We know that our enemy is this kind of vile murderer - not one another. We will use all of Sweden’s strength to track you down.
“Our message will always be clear: you cannot suppress us, you cannot control our lives, you will never win.”
Reports suggested a pram was caught in the path of destruction at around 3pm on Friday.
A nationwide manhunt was launched and police arrested the man in the Stockholm area.
Detectives said he appeared to match the description of a previously-publicised image of a man they wished to speak to.
Prosecutor Mr Ihrman called for him to be held over “terrorist crimes through murder” after police said he was under prolonged questioning.
The latest outrage inflicted on the continent came just two weeks after similar tactics were used to attack London, when Muslim convert Khalid Masood drove into crowds on Westminster Bridge.
The bloodshed also bore hallmarks of attacks seen in Nice and Berlin last year.
Swedish border controls were reinforced following the attack and investigators remained at the scene after the lorry was removed.
Condemnation poured in as news of the attack broke, including statements from German chancellor Angela Merkel and Foreign Secretary Boris Johnson, who said he was “deeply concerned”.
EU Commission president Jean-Claude Juncker said: “An attack on any of our member states is an attack on us all.”
The Aftonbladet newspaper reported that the truck had been hijacked from Swedish beer maker Spendrups earlier on Friday.
Witness Jan Granroth told the paper that “we stood inside a shoe store and heard something ... and then people started to scream”.
Mikael Anttila, a 49-year-old portfolio manager at bank SEB, told the Press Association he saw several hundred people gathered on the street close to the shop before they all started running “suddenly ... like ants”.
“Then a lot of police started coming. Heavy weapons, civilian police, etc,” he said.