The other member of the trio, Rachid Redouane, a 30-year-old who had claimed to be Moroccan and Libyan, was not known to intelligence services.
May faced a barrage of questions Monday on deep cuts made to police numbers in the United Kingdom while she was Home Secretary.
At about 10pm on Wednesday officers from the Met's counter-terrorism command, along with firearms officers, arrested two men on a street in Ilford, east London, while a third was arrested after a warrant was carried out at a home in Ilford.
"That is a question that will need to be answered by MI5, by the police, as the investigation goes on", he said.
Fusilier Rigby (right) was attacked by two jihadists who used a vehicle and knives to kill the off-duty soldier in Woolwich, South East London in May 2013.
In Britain's third terror attack in as many months, Butt and two others rammed a van into pedestrians on London Bridge on June 3 evening before running into the bustling Borough Market area where they slit throats and stabbed people. Volunteer your time and labour or donate to a homeless shelter. A Canadian, a French national and a Briton were among the dead, while other French people, a Spaniard, Australians and a New Zealander were among the 48 who were injured in what Prime Minister Theresa May called "an attack on the free world".
But she said "terrorism breeds terrorism" and that the perpetrators are "copying one another".
The two main candidates for prime minister - the incumbent, May, and the challenger, Jeremy Corbyn - traded barbs Monday over how security services can better protect the public after three mass-casualty attacks in as many months.
May defended her government's stance on the issue, saying that her Conservative government had protected police budgets.
The police apparently shoot the suspects after they seemingly refuse to surrender.
Christine Archibald with her fiancé, Tyler Ferguson.
Thomas was walking with his girlfriend over the bridge when the attack began on Saturday night.
Another 36 men and women are now in hospital, 18 of whom are in a critical condition, according to NHS England.
ISIS claimed responsibility for the attack on Sunday night, although they provided no evidence for their involvement or details of the attack.
Details of the investigation had been kept closely under wraps, in stark contrast to last month's Manchester bombing, when photos and information from the investigation were repeatedly leaked to the U.S. media, triggering a row between the British and American governments.
A man has been arrested on suspicion of terror offences by detectives investigating the London Bridge attack following an early morning raid at an address in east London.
Neighbours described Butt as an avid weightlifter. She said she thought he might have gone into hiding because she was aware he knew one of the slain attackers.
"We are not kids in playground".
"I understand deep down, inside my heart, the pain of these people", she said, speaking at her home near the northern city of Bologna.