Former London mayor Boris Johnson has said questions need to be answered over how one of the London attackers was monitored.
Counter-terror agencies are facing scrutiny after it emerged that Khuram Shazad Butt was investigated in 2015, but was "prioritised in the lower echelons of our investigate work" after officers found no evidence to suggest an attack was being planned.
The Foreign Secretary told Sky News: "People are going to look at the front pages today and they're going to say 'how on Earth could we have let this guy or possibly more through the net?'
"'What happened, how could he possibly be on a Channel 4 programme and be committing atrocities like this?'
"That is a question that will need to be answered by MI5, by the police, as the investigation goes on."
Metropolitan Police Assistant Commissioner Mark Rowley defended the actions of the security services.
He said: "At any one time MI5 and police are conducting around 500 active investigations, involving 3,000 subjects of interest.
"Additionally, there are around 20,000 individuals who are former subjects of interest, whose risk remains subject to review by MI5 and its partners."
Butt, who also went by the name Abu Zaitun, was allegedly an associate of radical hate preacher Anjem Choudary and was also reported to the anti-terror hotline in 2015 for showing signs of "extremism or radicalism", Mr Rowley said.
Transport for London confirmed Butt worked for London Underground for just under six months as a trainee customer services assistant, but left in October last year.
Meanwhile, the chairman of the mosque where one of the London attackers worshipped has told of his shock.
Sunawar Ali said that he remembered Rachid Redouane as "quiet" and "gentle".
Mr Ali said he had last seen Redouane about two weeks ago but he did not speak to him, nor did he see anyone else speak to him.
Redouane has been named by police along with Khuram Shazad Butt as two of the three terrorists responsible for killing seven people and injuring more than 40 in the London Bridge area on Saturday night.
He told Sky News that Redouane was "quiet ... hasn't made any problems".
When he was told Redouane, 30, had been involved in the terror attack, he said: "Wow, I feel very sad but I don't believe how this happened.
"I've got no clue why and how so really I'm shocked now.
"This sort of thing... security should be updated if this is the fact."
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Redouane claimed to be Moroccan and Libyan but was also known to have lived in the Rathmines area of Dublin, Ireland, for 18 months until last year.
Security sources in Ireland confirmed Redouane married a British woman in Dublin in 2012 and also went by the name Rachid Elkhdar.
The third attacker is yet to be publicly named by police and officers have appealed for people with information about the three men to come forward, especially anyone who can help piece together their movement in the days and hours leading up to the attack.
As well as using a van and knives in their murderous spree, the men are also believed to have had a stock of at least a dozen Molotov cocktails in the back of that van.
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Sky's Crime Correspondent Martin Brunt said: "Officers discovered what appeared to be bottles filled with a colourless liquid with rags coming out of the top, they clearly appeared to be Molotov cocktails."
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