The men's rampage followed a suicide bomb attack which killed 22 adults and children at a concert in Manchester two weeks ago, and an attack in March when five people died after a van was driven into pedestrians on London's Westminster Bridge.
Dozens of others were injured during the attack, including four police officers.
British police have named the third London attacker as Youssef Zaghba, a Moroccan-Italian who is reported to have been stopped at an airport in Italy on suspicion that he was bound for Syria.
The alert to the British authorities was a routine communication about a potential suspect, rather than an emergency red flag, according to the Italian security sources.
Zaghba lived in Morocco for much of his life but had made short visits to Italy to see his mother in Bologna.
Meanwhile, police on Tuesday also raided the homes of relatives of one of the London attackers in Pakistan, as it emerged he used to work for London Underground and had access to tunnels under the Houses of Parliament, British media reported Tuesday.
The latest person arrested is a 27-year-old man, detained Tuesday morning under Britain's Terrorism Act.
A new search was underway today in Ilford, just north of Barking, as authorities tried to determine whether the group had accomplices. The assault was the third attack in three months in which most of the assailants had been on authorities' radar at some point.
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The Islamic State took responsibility for the attack, though British officials have yet to confirm the militant group's involvement.
Security has become the number one issue and both main parties issued statements on Tuesday portraying their own positions on policing and intelligence as the most robust.
"However, there was no intelligence to suggest that this attack was being planned and the investigation had been prioritised accordingly", police said.
Redouane was 30 and "claimed to be Moroccan and Libyan". Authorities suspect Butt was radicalized in the United Kingdom and not in Pakistan, the newspapers said.
So far, 13 people have been arrested as part of police investigations and 12 have been released without charge.
Corbyn's party colleague, London Mayor Sadiq Kahn, told Britain's Channel 4 News that the police force is underfunded.
"Specialist officers from the Marine Police Unit and the Royal National Lifeboat Institution (RNLI) have been searching the river since the night of the attack".
Prime Minister Theresa May, who called the snap election in hopes of strengthening her mandate for discussions over Britain's exit from the European Union, has come under fire for the cuts to police numbers in recent years.
The number of police officers in England and Wales fell by nearly 20,000 between 2010 and 2016 - years when May, as home secretary, was in charge of policing.
Anyone who has seen him since June 3 or was present on the bridge at the time is asked to ring police on 0800 0961 233.