Although the Italian government notified the British and Moroccan governments about its concerns, Mr. Zaghba was not arrested. Recently, he was living in Britain and working at a restaurant in London.
The developments are likely to add to pressure on the British government over its monitoring of Mr. Butt, a British citizen who immigrated from Pakistan as a child. The London police, however, said that Mr. Zaghba “was not a police or MI5 subject of interest,” referring to Britain’s domestic intelligence agency.
Mr. Butt was one of an estimated 3,000 people in Britain who are under surveillance for jihadist activity, and he even appeared briefly in a Channel 4 documentary, “The Jihadis Next Door.” He was apparently deemed not to pose an immediate risk, however, and he was not one of the roughly 500 people at the center of active terrorism investigations.
On Tuesday, Transport for London, which runs the city’s public transit system, confirmed that Mr. Butt had worked for the London Underground “for just under six months as a trainee customer services assistant, leaving in October last year.”
Mr. Butt became increasing religious shortly before his marriage in 2013, said Nasir Dar, a maternal uncle of his, in an interview in Jhelum, Pakistan.
“For 23 years, he lived in Britain and visited Pakistan only twice, for a few weeks,” Mr. Dar said.
But a few months before the marriage, he recalled, “I noticed that he grew a beard and started to dress like the Arabs. When I inquired about this change in attire, he replied that he feels comfortable in that dress.”
Mr. Butt married the sister of a friend he met in Britain, the uncle said.
Mr. Dar, who owns a restaurant in Jhelum and said he was briefly questioned about his nephew by Pakistani intelligence officers Tuesday morning, said he had been shocked and saddened by the act his nephew carried out.
“Our religion does not allow killing people,” he said. “My heart goes out to those innocent people who were killed.”
The Times of London reported on Tuesday that Mr. Butt had links to an important contact of Mohammad Sidique Khan, one of four suicide bombers who killed 52 people in coordinated attacks on London’s transit system on July 7, 2005, and to Anjem Choudary, a radical preacher who is now serving a five-year prison term.
Mr. Choudary is considered one of the most successful recruiters of British Muslims to extremist groups. Mr. Butt is reported to have been involved in Al Muhajiroun, an organization that Mr. Choudary had led.
Born in the London area, Mr. Choudary spent nearly two decades as a radical preacher who influenced young people through speeches as well as personal contacts — creating what Peter R. Neumann, a professor of security studies at King’s College London and director of its International Center for the Study of Radicalization, called “a sense of community, belonging and camaraderie within a circle of peers.”
Several of Mr. Choudary’s organizations were banned, including Al Muhajiroun, which he had founded with the radical cleric Omar Bakri Mohammed, who fled Britain for Lebanon, and Islam4UK, proscribed as a terrorist organization in 2010.
Mr. Choudary is considered responsible for recruiting several hundred people to travel to the Middle East to fight for Al Qaeda and the Islamic State, and for inspiring those who killed the British soldier Lee Rigby, who was hit by a car and then attacked with a meat cleaver outside his barracks in southeast London in 2013.
Foreign Secretary Boris Johnson, a leading member of the governing Conservative Party, acknowledged in an interview on Tuesday that the public was asking tough questions about how Mr. Butt’s case had been treated by the authorities.
“How on earth could we have let this guy or possibly more through the net — what happened?” he asked in an interview on Sky News. “How can he possibly be on a Channel 4 program and then committing atrocities like this, and that is a question that will need to be answered by MI5, by the police as the investigation goes on.”
The revelations are particularly awkward for the party’s leader, Prime Minister Theresa May, who as home secretary from 2010 to 2016 was in charge of domestic security and defended cuts in policing that are now being attacked by the opposition Labour Party.
Salman Abedi, the bomber who killed 22 people in Manchester, England, on May 22, was referred to the police numerous times as someone with radical views — much as Mr. Butt was — but the police decided in both cases that the men were not a serious or imminent threat. MI5 is now investigating whether it missed warning signs.
Mrs. May told Sky News on Tuesday, after Mr. Johnson spoke, that she expected the London case to go through a similar review. “MI5 and the police have already said they would be reviewing how they dealt with Manchester, and I would expect them to do exactly the same in relation to London Bridge,” he said.
According to Mr. Neumann and his deputy at the center for the study of radicalization, Shiraz Maher, Mrs. May’s push to deny “the safe space” of the internet to Islamist radicals underestimates the power of personal contact, as very few terrorists are recruited solely online.
Use of the internet is common for recruitment, but it nearly always requires personal contact — an individual, like Mr. Choudary, “who creates a sense of social obligation and group pressure,” Mr. Neumann said.
The commissioner of the Metropolitan Police, Cressida Dick, said on Monday that the authorities had uncovered 18 jihadist plots since 2013 — five of them since March — and that “all the recent attacks have a primarily domestic center of gravity,” meaning that while they might have been inspired by overseas extremists, they had little contact with or instruction from them.
There are reports that Mr. Butt and his brother were also involved in the British program Prevent, which seeks to stop people from becoming terrorists or supporting terrorism, and which refers people suspected of radicalization to programs led by the police.
Many Muslims are suspicious of Prevent because of that police involvement. In other countries, like Germany and the Netherlands, such programs are led by local government or by nongovernmental institutions. Critics have said that if the goal is to better integrate Muslims into society, having police and domestic security officials take the lead is the wrong strategy — because Muslims fear that the programs are intended to spy on them, not help them.
Two of the seven victims of the London attack have now been officially identified. The first was Christine Archibald, known as Chrissy, a Canadian who lived in The Hague and was visiting London. On Tuesday, the police formally identified a second victim: Kirsty Boden, an Australian nurse who had been reported missing.
Britain observed a moment of silence at 11 a.m. on Tuesday to remember the victims of the attack, even as the investigations continued.
Around 1:30 a.m., the authorities raided a property in an East London neighborhood, Ilford, and at 8:05 a.m., a 27-year-old man was arrested in Barking, the East London neighborhood where Mr. Butt lived. Twelve people who were arrested on Sunday in Barking have been released without charge.