The British man who was killed in the Sweden lorry attack has been named as 41-year-old Chris Bevington.
Two Swedes and a Belgian national were also killed when a hijacked lorry ploughed into pedestrians in Stockholm on Friday.
Rakhmat Akilov, a 39-year-old man from Uzbekistan, has been arrested on suspicion of "terrorist crimes through murder".
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.
The main suspect in the Stockholm lorry attack has admitted to carrying out a terror crime, his defence lawyer said.
The Ahlens department store in Stockholm apologised "for a bad decision" in promoting the offer.
The British man who was killed in the Stockholm lorry attack has been named as Chris Bevington.