BBC Breakfast

Metropolitan Police Commissioner Cressida Dick says police believe they know the identity of the attackers and the priority now is to find out whether they were working with anybody else.

There are 12 people in custody following raids and police have "seized a huge amount of forensic material", she tells BBC Breakfast.

The Met will "roll out proper protection across London for individuals, for events", she adds.

"It is a very large-scale response."

Taxi drivers were some of the first people trying to help - and warn - people during the attack.

LBC has spoken to a couple, external, including Chris who described how he tried to run over one of the attackers.

"I told people to turn around and run away. It sickened me to the pit of my stomach. An absolute animal," he said, while Paul said initially he thought someone had been knocked off their bike.

Other heroes on the night include Carlos Pinto, 33, a critical care nurse who helped a woman who was stabbed in the chest in a restaurant.

While Gerard Vowls told the BBC how he tried to stop the attackers stabbing a woman. He threw bottles, pint glasses and chairs at the men.

Image source, Carlos (left) and Giovanni were in a restaurant where an attacker stabbed a woman

Today Programme
BBC Radio 4

Image source, PA

Labour's Yvette Cooper, the former chair of the Home Affairs Select Committee, says she agrees with party leader Jeremy Corbyn that "police cuts have gone too far".

She pays tribute to the emergency services who responded to the attack, telling Today: "The armed response to the attack in London was phenomenal."

However, she adds: "To lose 20,000 officers wasn't the right thing for our future and we should be trying to increase them again."

Immediately after the attack, people across the capital were offering help to those affected by sharing the hashtag #SofaForLondon on social media.

Taxi drivers provided free rides from the cordons around London Bridge and Borough Market that left many cut off.

Places of worship across many faiths joined pubs, hotels and businesses in providing food and shelter.

Strangers reached out on social media offering a cuppa, chat or spare bed for the night.

Image source, PA

Image source, Getty Images

A neighbour of one of the three London Bridge attackers said he had reported him to police.

The man, who did not wish to be identified, said: "We spoke about a particular attack that happened and, like most attackers, he had a justification for everything.

"So it was then I realised I had to speak to the authorities."

Labour's Emily Thornberry tells BBC Breakfast that London is "a really strong city - we are an example to the world.

"There is a resilience to London that we have shown throughout the decades."

The shadow foreign secretary says there is not one thing that will solve the terrorist threat but adds that "police are very stretched - it's quite clear we don't have enough officers".

She highlights Labour's manifesto pledge to create 10,000 new police officers over the course of the next parliament.

In the year ending 31 March 2016, there were 255 terrorism-related arrests, leading to 37 prosecutions.

Prime Minister Theresa May has said the UK must adapt to a new type of terrorism - but what powers do the police and security services have at the moment?

Reality Check has been looking at the current measures to stop potential terrorists.

BBC Radio 5 live

Labour leader Jeremy Corbyn has criticised police cuts and accused the Conservatives of trying to "protect the public on the cheap".

Culture Secretary Karen Bradley defends the government's record on 5 Live: "If you go back to 2010, you'll remember that there was no money and all parties agreed that there had to be savings."

She claims that "crime fell by a third since 2010 because the police do excellent work".

Returning to the number of anti-terror bills that Parliament has passed, she says: "Jeremy Corbyn voted against every single one of them."

BBC Radio 5 live

"My heart goes out to everybody affected," says Culture, Media and Sport Secretary Karen Bradley, who joins 5 Live Breakfast.

Presenter Nicky Campbell reads a long list of counter-terrorism legislation and asks what comes next.

The cabinet minister argues that we now see "terrorism breeding terrorism" and it must be tackled in four main ways: confronting the ideology, tackling "safe spaces" online, addressing segregation in society, as well as counter-terrorism measures.

Ms Bradley says that "eight plots, of which three got through, is an unprecedented scale".

BBC London Travel
BBC Radio London Travel

London Bridge station has reopened after being closed as a result of Saturday's attack.

A police cordon around the station was lifted at 05:00 BST, meaning that Monday morning services should be largely unaffected.

The northbound carriageway of London Bridge has also been opened to traffic and pedestrians, but the southbound part of the bridge remains closed.

A police operation continues in the London Bridge and Borough Market area, where three attackers killed seven people.

Borough High Street up to Great Dover Street remains closed.

BBC London's Jason Rosam is speaking to people in Borough High Street all morning - you can listen to his reports on the Vanessa Feltz breakfast show.

Today Programme
BBC Radio 4

Image source, PA

The BBC's assistant political editor, Norman Smith, observes that the political "ceasefire in the wake of London Bridge broke down within hours".

Theresa May made her "enough is enough" speech on Sunday and Jeremy Corbyn accused Mrs May, in turn, of trying to protect the public "on the cheap".

Norman says this is a sign of "how deep and, frankly, tribal are the divisions" over counter-terrorism and counter-extremism.

• The Met Police says it knows who the attackers are and will release their identity "as soon as operationally possible"
• The first victim has been named as Canadian national Chrissy Archibald
• The so-called Islamic State group has said it was behind the attack
• Two addresses in east London - one in Newham and another in Barking - are being searched by officers
• London Bridge rail and Tube stations both reopened for entry and exit as have the bridge and surrounding roads
• Prime Minister Theresa May will chair a meeting of the government's emergency committee Cobra on Monday morning
• There will be a minute's silence on Tuesday at 11:00 BST in remembrance of those who lost their lives and all others affected by the attacks
• A French national was killed and seven others wounded, including four with serious injuries according to foreign minister Jean-Yves Le Drian. One French national is still missing
• The Met Police has set up a casualty bureau on 0800 096 1233 and 020 7158 0197 for people concerned about friends or relatives

This is a summary of what we know so far about the attack.

Today Programme
BBC Radio 4

BBC home affairs correspondent Danny Shaw tells the Today programme there will be concerns over three terrorist attacks in three months, that may all have been committed by people who were "somewhere on the radar" of the security and intelligence services.

Following the Manchester attack last month, the terror threat level was raised to "critical" because the authorities believed that more people connected with the plot were at large.

The authorities do not believe this is the case following the London Bridge attack and the threat level remains at at "severe".

Security barriers have been installed on some bridges in central London overnight to protect pedestrians from road traffic.

The barriers were installed on Lambeth Bridge, Waterloo Bridge southbound and Westminster Bridge in both directions, where Khalid Masood killed five people in March before being killed himself.

On Sunday Assistant Commissioner Mark Rowley said there would be "increased physical measures on London's bridges to keep the public safe".

BBC Breakfast

For the second time in a very short election campaign, there has been a pause in national campaigning following a terrorist attack, BBC political correspondent Chris Mason tells Breakfast.

But by this morning there was a definite resumption in campaigning with some "spiky remarks" from Labour leader Jeremy Corbyn about police cuts - and Theresa May's record as home secretary before she became PM.

Mrs May, meanwhile, will set out more about proposals for tougher sentences and cracking down on internet companies.

And Liberal Democrat leader Tim Farron has written an article for the Guardian, external calling for more to be done "to tackle the sources of terrorist funding", Chris adds.

Adapting a phrase used by the prime minister following the attacks, the article says "difficult and embarrassing conversations with those such as Saudi Arabia" might be necessary.

London Bridge rail and Tube stations have both reopened for entry and exit.

National Rail said the police cordons in the area of the attack had been lifted earlier than expected so London Bridge itself was open as well as the surrounding roads.

Police say officers are searching two addresses in east London - one in Newham and another in Barking.

Scotland Yard added that a number of people had been detained.

Dave Lee
North America technology reporter

Image source, Getty Images

Tech companies and experts have defended the work they do in fighting extremist content on their networks.

It comes after Theresa May said areas of the internet must be closed because tech giants provided a "safe space" for terrorist ideology.

Google - which owns video site Youtube - said it had invested hundreds of millions of pounds to tackle the issue.

Facebook said it worked aggressively to remove content quickly - adding that it wanted to make the site a hostile environment for terrorists.

Last year, the website enabled end-to-end encryption on its messaging apps such as WhatsApp. Apple did the same with its app, iMessage.

It has made it almost impossible for police to intercept and read messages unless a user unlocks their phone.

People, including reporters, took to Twitter to share touching videos of officers dancing with children at the One Love Manchester concert.