A search warrant was executed at a property in Bedfordshire, under the Terrorism Act 2000, on Sunday night, the Metropolitan Police said.
It follows the suspected suicide and car bombing in Stockholm on Saturday.
Unconfirmed reports say the man killed by the blast was Taimour Abdulwahab al-Abdaly, 29, who lived in Luton.
Scotland Yard said no arrests had been made and no hazardous materials had been found at the property, the exact location of which has not been released. The search is expected to resume later.
A Home Office spokesman said: “We remain in close contact with the Swedish authorities. It would be inappropriate to comment on their ongoing investigation at this time.”
Several newspapers, Swedish websites and an Islamist forum have named Abdaly, an Iraqi-born Swede, as the attacker.
It is believed he blew himself up after he had tried to set off a car bomb in a busy street. Two people were injured.
BBC security correspondent Gordon Corera says it is likely the British security services will be investigating how long Abdaly spent in the UK and the significance of that time, as well as establishing whether he was connected to other individuals.
Abdaly listed himself on Muslim dating website Muslima as a physical therapy graduate from Bedfordshire University. There has been no comment from the university.
In his profile on the site, Abdaly says he was born in Baghdad and moved to Sweden in 1992, before arriving in the UK in 2001 to study.
He says he was married in 2004 and had two young daughters.
“I want to get married again, and would like to have a big family. My wife agreed to this,” he wrote.
The Daily Telegraph quotes his neighbours as saying they last saw him two-and-a-half weeks ago.
Tahir Hussain, 33, a taxi driver who lives nearby, told the paper: “I used to see him around often. He didn’t say much but seemed nice. I used to see him walking with his kids.
“I was shocked when I heard what happened because I never thought he could do such a thing.”
The car blew up in a busy shopping street in the area of Drottninggatan at 1700 (1600 GMT) on Saturday and the second blast occurred 10 to 15 minutes later on a street about 300m away, Swedish police said.
Witnesses said a man found dead after the second blast had been carrying an explosive device.
Swedish PM Fredrik Reinfeldt said the attacks were unacceptable in Sweden’s “open society”, which he said was a democracy that respected different cultures.
The country’s police are investigating a set of e-mails sent shortly before the blasts threatening attacks because Sweden had sent troops to Afghanistan.
Sweden has 500 soldiers deployed in Afghanistan as part of the international military force.
The e-mails, with MP3 audio files in Swedish and Arabic, were sent to the Swedish security service and the TT news agency.
They called for “mujahideen” – or Islamist fighters – to rise up in Sweden and Europe, promising Swedes would “die like our brothers and sisters”.
They also attacked the country for caricatures of the Prophet Muhammad drawn by Swedish artist Lars Vilks.
If confirmed as a suicide bombing, the attack would be the first of its kind in Sweden.