Police say the death toll from Saturday's attacks has risen to eight
Australian au pair Sara Zelenak is named as the latest victim of the attacks
Police searching for French national Xavier Thomas have recovered a body from the Thames
A 30-year-old man was arrested for terrorism offences in the early hours of Wednesday
Police casualty bureau can be contacted on 0800 096 1233 and 020 7158 0197
Image source, H.AttaiThe BBC is bringing you all the news on the London Bridge attack as it happens.
To keep up-to-date with everything we know so far and all our news, features and analysis, click here to see our special report.
Elizabeth O'Neill, mother of Daniel O'Neill, who was stabbed in last night's attack, has been speaking to the BBC.
She said her son, 23, who is recovering in hospital, has a seven inch scar from the knife attack.
"He had just stepped outside the bar for a second and a man ran up to him and said 'this is for my family, this is for Islam' and put a knife in him," Ms O'Neill said.
"I'm still in shock. I can't quite believe it's happened.
"These people say they are doing this in the name of God which is an absolute joke.
"They are callous they are barbaric and they are absolute cowards. We will carry on as normal."
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A Question Time election special featuring SNP leader Nicola Sturgeon and the Lib Dems' Tim Farron in Edinburgh that had been due to be broadcast later has been rescheduled.
Nick Robinson will now present the programme at 21:00 BST on Monday on BBC One.
It was moved from Sunday evening after the London attacks, as most political parties suspended their national campaigns.
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The PM says online spaces used by terrorists must be shut down
Joe Lynam
Business correspondent
Calling for technology companies to "do more" has become one of the first responses by politicians after terror attacks in their country.
Theresa May's comments on that subject were not new - although the tone was.
She has already proposed a levy on internet firms as well as sanctions on firms for failing to remove illegal content, in the Conservative party manifesto published three weeks ago.
Given that 400 hours of videos are uploaded onto YouTube every minute and that there are two billion active Facebook users, clamping down on sites which encourage or promote terror needs a lot of automatic detection using software as well as the human eye and judgement.
Following criticism of the London mayor by US President Donald Trump, politicians from other parties have been expressing support for Sadiq Khan.
Lib Dem leader Tim Farron: "Sadiq Khan has shown calm and dignified resolve in the face of these cowardly terrorist attacks. He is more of a statesman than Donald Trump will ever be."
Conservative minister Penny Mordaunt tweeted:
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A student nurse who escaped last night's attack says she wants to find the taxi driver who saved her life.
Rhiannon Owen was on Borough High Street getting cash out when a passing cabbie shouted for her to run.
She managed to find shelter in a nearby pub, alerting them to the attack, and now believes the actions of the unknown man saved her life.
"I don't know who you are, but you saved my life. I could run away because you told me to. Whoever you are I want to say thank you so much."
The BBC's Rich Preston tweets some context to the news of 50 rounds fired:
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Additional police, both armed and unarmed, will be seen across London this week, says Mr Rowley, and policing plans for forthcoming events will be looked at again.
He also confirmed there will be increased security measures on bridges across the city to keep people safe.
Assistant Commissioner Mark Rowley said the cordon in place around London Bridge and Borough Market will be there for "some time yet" and could impact the Monday morning rush hour.
He advised people to check with their travel operators and seek alternative routes where possible.
He also asked the public to avoid the area for the moment as officers carry out their work.
Mr Rowley confirmed that a member of the public had been shot during the operation and was receiving treatment in hospital.
Police are working on informing all the next of kin of the victims, but Mr Rowley said it may take some time as they believe some of them were from abroad.
Eight police officers fired a total of 50 bullets to kill the three London Bridge attackers, Metropolitan Police Assistant Commissioner Mark Rowley said.
He described it as an "unprecedented" number of shots fired by police.
An IPCC investigation would take place, but he said that the situation officers faced was "critical".
He said he was "humbled by the bravery of officers who will rush towards a potential suicide bomber".
Image source, Getty ImagesLast night's attack in London Bridge is sadly the latest of several terror incidents in Great Britain over the past decades.
Click here to see a timeline of attacks and attempted attacks.
A neighbour of the Barking flat believed to belong to one of the attackers has described him as "very much a member of the community".
Damien Pettit (above) said the man had been "very family-orientated" and that his wife had just had another child.
Reports that the he had been one of the London Bridge attackers were "very hard to understand", he said.
Furqan Nabi, who also lives in the area, said he used to see the man playing table tennis in the lobby of the building and playing with his children.
There are reports of a heavy armed police presence in East Ham - a mile away from where police raided a block of flats linked to last night's attack.
They have been seen on Barking Road, but Scotland Yard was unable to say whether it was linked to the 12 arrests made after the raids.
Canadian Prime Minister Justin Trudeau has confirmed that a Canadian national was among those killed in last night's terror attack in London Bridge.
Mr Trudeau condemned what he called a "senseless attack" and said he was "heartbroken" that a Canadian was among those killed.
"We grieve with the families and friends of those who have lost loved ones, and wish all those injured a speedy and full recovery," he added.
"Londoners and people across the United Kingdom have always displayed strength and resilience in the face of adversity. This time will be no different.
"These hateful acts do not deter us; they only strengthen our resolve. Canadians stand united with the British people. We will continue to work together with the United Kingdom and all our allies to fight terrorism and bring perpetrators to justice."
The prime minister has paid a private visit to victims of last night's the terror attack.
Theresa May went to King's College Hospital in south London this afternoon, which has been caring for 14 patients, to meet victims and the staff who are treating them.
New figures from NHS England show that of the 48 people taken to hospital on Saturday night, 36 are being cared for in central London hospitals.
The Royal London Hospital is looking after 12 patients, while St Thomas' Hospital has four, University College Hospital has five and St Mary's Hospital has one.
Image source, PAThe former independent reviewer of terrorism legislation says Theresa May could be looking to reintroduce control orders when she reviews the UK's anti-terrorism strategy.
Lord Carlile of Berriew said if they had been in place, they "may have saved a lot of lives".
Control orders were introduced by Tony Blair in 2005. The orders allowed suspects to be relocated away from their home communities, subjected them to 16-hour home-arrest curfews and barred them from using mobile phones or the internet.
They were replaced by Terrorism Prevention and Investigation Measures or Tpims in 2011.
Lord Carlile said that internment of suspected extremists was "not a realistic option", as it would be ruled unlawful by the courts, and that there was "no evidence" to support any extension to the 14-day period which terror suspects can be held without trial, as it would be a "purely symbolic" measure.
He backed longer maximum sentences for offences like incitement of terror, conspiracy or "providing bed and board" to plotters, but he warned against mandatory minimum sentences, which could encourage juries to acquit rather than force a penalty they see as too harsh.
Paul Ashworth, from Surrey has been cycling around the London Bridge area giving out water to the police.
"I've just come to give the police some cold water. It's nothing in comparison to what they do. It's just to try and give something back. They're protecting us, saving our lives," he said.
The plumber, who cycled 35km from the Surrey border into London, said: "We've just to got to keep together - the whole world has."