London attack as it happened: Met Police make arrests during early morning raids in search for jihadi network
'Gunshots' heard as 'a number' of people arrested
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Police have named two of the three terrorists responsible for Saturday's deadly attack on London Bridge.
Khuram Shazad Butt, 27, and Rachid Redouane, 30, both from Barking, East London, were identified as the perpetrators of the knife and van attack, which killed seven people and left 49 injured.
Butt was previously known to security services but the Met Police said there was no intelligence to suggest the attack was being planned. Redouane was not known to authorities, Scotland Yard said.
Police detained a number of people in early morning raids in east London as part of the investigation into the London Bridge attack which saw the attackers ram a van into pedestrians on London Bridge before stabbing revellers in bars in the nearby Borough Market.
Isis claimed responsibility for the attack, the third major militant assault to hit Britain in less than three months.
Two of the seven people who were killed have been named, and 21 people remain critically injured in hospital.
A Canadian woman, who died in her fiance's arms after being struck by the speeding van, was named as 30-year-old Christine Archibald.
A 32-year-old man from Hackney, James McMullan, has also been identified as one of the victim's by his family.
Isis was said to have urged extremists to run over civilians in a poster released over the weekend featuring a knife, handgun and lorry urging radicals to "gain benefit from Ramadan".
The three men, wearing fake suicide bomb vests, were shot dead by eight officers outside a pub after police opened fire with an "unprecedented" hail of 50 bullets, while a bystander was also shot.
Scotland Yard said seven women and five men aged between 19 and 60 were arrested under the Terrorism Act in Barking on Sunday. A 55-year-old man was later released without charge.
A vigil was held on Monday evening near London Bridge in honour of the victims of the attack, which took place at around 10pm, while a minute's silence will take place at 11am on Tuesday.
Sadiq Khan told mourners: "As Mayor of London I want to send a clear message to the sick and evil terrorists who commit these crimes: we will defeat you you will not win.
"As a proud and patriotic British Muslim, I now say this: you do not commit these disgusting acts in my name."
Network Rail said London Bridge rail and London Underground stations reopened at 5am but the rail station will be exit only.
People from around the world were caught up as hundreds cowered in pubs and restaurants, barricading themselves inside as the attackers stalked the streets.
Tales of heroism emerged in the aftermath, with one British Transport Police officer taking on the trio armed only with his baton before being stabbed in the head, face and leg.
An off-duty Metropolitan Police officer was also injured after he tackled the men.
Forty-eight people were left in hospital, 21 critically injured.
As counter-terrorism police units and security services launched a huge investigation for the third time in a matter of weeks, officers arrested a dozen people in raids on flats in Barking, east London, where residents said they believed one of the terrorists may have lived.
One neighbour said one of the attackers had recently asked him how he could hire a van.
Asked if police cuts were raised while she was Home Secretary, Ms May said she thinks the Government needs to take a "much more robust" approach to extremism.
"I think we have seen too much tolerance of extremism in our society," the Prime Minister said.
When asked if she accepts she was wrong to call those who are concerned about cuts to policing "crying wolves," Ms May repeated her claim the Government has protected counter-terrorism policing and protected police budgets from 2015. She also attacked Jeremy Corbyn in the same way she did earlier.
Responding to a question about whether she had changed her mind on how to tackle extremism ideology, Ms May said she had been clear it isn't just about violent extremism but is about extremism.
She said as Home Secretary she introduced the counter-extremism strategy and has said over the years Britain needs to deal with extremism, not just violent extremism.
"While we've made progress in relation to extremism, I believe there has been overall too great a willingness to tolerate extremism in our society."
What's your message to those who say Britain is cowering in the face of terror?
Get on with life, it's business as usual, Ms May said.
"People here in the UK are going about their business because we will not allow the terrorists to defeat us. We will defeat them."
Do you regard these attacks as a failure to prevent the attacks by the Government? Do you worry about what that says about your record?
The police and security services have foiled five other attacks, Ms May said.
It's absolutely right to look at our response and adjust it as we see the terror threat evolving.
Police have now identified all three attackers, Ms May said. She said she cannot comment on the individuals.
What would Donald Trump have to say for you to criticise him publicly?
I think President Trump is wrong to have taken America out of the Paris climate change agreement, Ms May said.
She reiterated that she thinks Sadiq Khan, the Mayor of London, is doing a good job.
Theresa May's news conference has now finished. She refused to say she regrets cutting police numbers while she was Home Secretary.
Speaking from inside the Cabinet Room at 10 Downing Street earlier, Ms May said the police had "put additional security measures in place to protect the public and provide reassurance and this includes additional security measures at a number of bridges in London".
The Prime Minister's comments on policing came after she was accused by Mr Corbyn of denying police and security services the resources they need while suppressing evidence of Saudi support for violent extremists.
The Labour leader used a speech on Sunday evening to warn that the Government could not "protect the public on the cheap", and said she had cut police manpower by 20,000 despite warnings that this would undermine safety.
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