A police cordon surrounded the neat-looking terraced house in Luton, a town with a large immigrant population to the north of London where Taimour Abdulwahab lived, apparently with his wife and three children.
British police said no arrests had been made and no "hazardous materials" had been found. Press reports said neighbours last saw him at the house two weeks ago.
"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," said Tahir Hussain, 33, a taxi driver in the town.
Abdel Wahab was reportedly born in Iraq before moving to Sweden in 1992.
In 2001, he moved to Britain to study sports therapy at the University of Bedfordshire from 2001 to 2004, but had been working recently at a carpet shop.
The university released a statement saying that a student of the name of Taimour Abdulwahab, described as a Swedish national, "registered in 2001 and graduated with a BSc in sports therapy from the University of Luton in 2004."
The vice-chancellor of the University of Bedfordshire, which used to be called the University of Luton, was to give a news conference later Monday.
Reports in Britain said his wife is called Umm Amira, known as Mona, and runs a company called Amira Makeup and Hair which offers services including bridal make-up and hair styling.
Many reports said the man had been looking for a second wife on an internet dating site, describing himself as "very religious" and saying that he was considering moving to an Arabic-speaking country in the future.
British police are said to be investigating reports that he was radicalised at the university.
The case has echoes of Umar Farouk Abdulmutallab, the Nigerian student who tried to blow up a US-bound airliner with explosives in his underwear, who investigators believe was radicalised while studying at university in London.
The town of Luton has been a focal point of clashes between Islamic and far-right extremists in recent years. In 2009, it fell under the spotlight when Muslim extremists demonstrated at a homecoming march for British soldiers of the Anglian Regiment returning from Afghanistan.
They held placards calling the troops "Anglian Soldiers: Butchers of Basra" and "Anglian Soldiers: cowards, killers, extremists."
In 2005, the four suicide bombers who killed 52 people on London's transport system met up at Luton to make their way into the capital.
The town has recently become a centre of activity for the anti-immigrant far-right English Defence League.
A spokesman for London's Metropolitan Police, which handles terror-related investigations anywhere in the country, confirmed a search was under way at the house.
"Officers executed a search warrant under the Terrorism Act 2000 at an address in Bedfordshire. We are confirming that this is in connection with the incident in Stockholm," the spokesman said.
Saturday's explosions came as Christmas shoppers thronged a busy pedestrian district of the Swedish capital. The man believed to be Abdulwahab was killed in one blast, while a car bomb exploded nearby and injured two people.
The website that named him as the perpetrator of the attack said: "It is our brother, mujahid Taimour Abdulwahab, who carried out the martyrdom operation in Stockholm."
Sweden's chief prosecutor Tomas Lindstrand said Monday investigators were almost certain the man who blew himself up in Stockholm was Abdulwahab. The man could not yet be named with certainty because DNA tests had not been performed and the family had not identified the body, he said.
The prosecutor said the man was born in 1981 in the Middle East and became a Swedish citizen in 1992. He was not previously known to Swedish intelligence.
British Prime Minister David Cameron had a telephone conversation with his Swedish counterpart Fredrik Reinfeldt at the weekend about the blast, Downing Street said.
"This was a discussion to update one another on the latest information surrounding this case. Clearly if there is any way we can support them, we will do," Cameron's spokesman said.