The Metropolitan Police have defended a decision to downgrade an inquiry into one of the men who carried out Saturday night's terror attack.
But despite receiving calls from concerned members of the public about Butt's increasingly radical views, police concluded he was not a threat and the investigation was scaled back.
Ms Dick said it was "certainly a possibility" that the attacks were triggering the next one. He and Butt lived in the same area of east London.
"At any one time, MI5 and police are conducting around 500 active investigations involving 3,000 subjects of interest".
A woman attaches a sign near London Bridge, after attackers rammed a hired van into pedestrians on London Bridge and stabbed others nearby killing and injuring people, in London, Britain June 4, 2017.
The Scotland Yard said one of them was Khuram Shazad Butt, 27, a Pakistan-born individual who had been investigated by MI5 and United Kingdom police.
"The security and intelligence services and police have stopped 18 plots since 2013, including five since the Westminster attack two months ago".
Hannah Stuart, author of Islamist Terrorism, a definitive analysis of United Kingdom attacks and offences, said: "Al-Muhajiroun is obviously very well known to both the police and to MI5".
Islamic State (IS) has claimed responsibility for the London Bridge rampage, while the attack has sparked fears that Britain is in the grip of a spate of copycat incidents.More news: Sportswriter loses job after 'disrespectful' Indy 500 tweet
Butt featured in a Channel 4 documentary previous year about Islamist extremists with links to the jailed preacher Anjem Choudary.
May insisted London police were happy with their resources, while counter-terrorism budgets had been protected and the number of armed officers had increased.
All 12 people arrested on Sunday after the London attack have now been released without charge.
May's main opponent, Labour leader Jeremy Corbyn, backed calls for her resignation over the police cuts.
He said many people were "very anxious that she was at the Home Office for all this time, presided over these cuts in police numbers, and now is saying that we have a problem". The IRA ran a 30-year armed campaign against British rule in Northern Ireland.
But May's own record came under fire from Labour, which - according to opinion polls questioned for their reliability - has closed the gap on her Conservatives ahead of Thursday's election.
Christine Archibald, a 30-year-old Canadian who had worked in a shelter for the homeless before moving to Europe to be with her fiancé, was the first of those who died to be named.
A vigil was held at London Bridge last night for the victims of the attack.
Before holding a minute's silence, Khan, the first Muslim to be elected mayor of a major Western European city, said: "I want to send a clear message to the sick and evil extremists who commit these disgusting crimes". Addressing the attackers, he said: "We will defeat you". All three have been claimed by the Islamic State in Iraq and Syria group.