Prime Minister Theresa May has spoken with her Swedish counterpart and offered to work together against extremist attacks.
Downing Street said she had expressed condolences on behalf of the British people in a telephone call to Swedish Prime Minister Stefan Lofven.
The statement said the two leaders agreed on the importance of working together to tackle such threats.
Britain was hit by a similar attack last month when a man drove a car into pedestrians before stabbing a policeman to death outside the Houses of Parliament.
Five of the 15 people who were injured in the Stockholm lorry attack have been released from hospital.
Sweden's health service said four of the 10 remaining were seriously injured and two are in intensive care.
It added that the one child still in Karolinska Hospital was not seriously injured.
Four people were killed when the driver of a hijacked truck ploughed into a group of pedestrians in central Stockholm on Friday.
Swedish police said they have arrested a man who is "likely" to be the culprit.
A man arrested following the deadly lorry attack in Stockholm is "likely" to be the driver of the hijacked truck which ploughed into pedestrians, Swedish Police said.
The man was detained in a northern Stockholm suburb on Friday and later arrested on suspicion of "terrorist crimes through murder".
Four people were killed after the beer lorry crashed into a department store in the Swedish capital on Friday afternoon.
"Yes, it is correct, it is likely him," police spokesman Lars Bystrom said on Saturday.
"The person in question has been arrested as the culprit, in this case the driver," he added.
The prosecutor, Hans Ihrman, said that the unidentified suspect should face a pre-trial custody hearing before midday on Tuesday or be released.
Officials also confirmed that only one person has been arrested in the case, contrary to media reports that two had been detained.
Beauty products remain on display yards from where a department store shop window was smashed in during Friday's deadly lorry attack in Stockholm city centre.
Swedish police have cordoned off the attack site and towed the vehicle away as an investigation gets underway.
Four people were killed after the hijacked lorry was driven along the pedestrianised street, Drottninggatan, in the busy shopping district before crashing into the Ahlens department store just before 3pm local time.
The lorry used in the suspected terror attack in Stockholm has been towed away from the central shopping street.
Swedish police said cordons around the crime scene would remain in place until the on-site investigation has been completed.
The first man arrested in connection with Stockholm's lorry attack is being held "on suspicion of terrorist crimes through murder", the office of the Swedish prosecutor has said.
It is the strongest degree of suspicion in Sweden's legal system, which can apply several different levels to hold a person.
Police confirmed he was now under "prolonged arrest".
The Stockholm lorry attack bears similarities to recent terror attacks in Westminster, Berlin and Nice.Read the full story ›
A second man has been arrested in relation to the deadly lorry attack on a Swedish department store, Sweden's national public broadcaster SVT has reported.
Police are said to believe he is connected to the other man who was arrested earlier.
SVT, citing police sources, said the man was arrested in the northern suburb Hjulsta.
The lorry crashed into shopping centre in Stockholm, killing at least four people, in what the Swedish prime minister has called a terror attack.
The whole of Sweden is "united in grief and anger" following the lorry attack which left four people dead and 15 injured, the country's Prime Minister has said.
"These kinds of actions will never succeed," said Stefan Lofevn.
"We know that our enemies are these atrocious murderers and not each other.
"Our message will always be clear: you will not defeat us, you will not govern our lives, you will never ever win."
Mr Lofven added that the country is "determined to never let the values we cherish be undermined by hatred" and called the crash an "act of terror".
The seconds before a lorry crashes into a department store in Stockholm have been captured on CCTV, showing people fleeing along Drottninggatan, a street in a busy shopping district, and into a shop.
Four people died after the lorry crashed into upmarket department store Ahlens, and 15 others were wounded, nine seriously.