"This is a fast-moving investigation". Police officers yelled at people to run from the area.
Attackers killed more than one person, according to media reports.
A massive manhunt was launched after the incident. A third suspect was believed to still be on the run.
There are also reports that a bystander was shot in the head in the crossfire and at least seven people have been stabbed.
London Bridge has been closed after an incident on Saturday night, after witnesses said a van had hit pedestrians.
Police say the incidents occurred on the bridge and at Borough Market a short distance away.
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She was just there, she was brilliant. "I think it's going to be a really long recovery process for them", she said. Evie's mum Karen said: 'She came in and she was just lovely, adorable and humble - and all over the girls.
Police also are reporting a potential incident in the Vauxhall area of southwest London. The Vauxhall stabbing is not connect to the incidents, they tweeted. He said he ran and hid, and was then told by police to run home.
"We are dealing with an incident on #LondonBridge, when we have more information we will update this twitter feed".
He also tweeted, "Whatever the United States can do to help out in London and the U". I want to express my huge gratitude to the police and emergency services who are on the scene.
Reuters television pictures showed dozens of emergency vehicles in the area around London Bridge. Police tweeted that Londoners should "remain calm but be alert and vigilant". British Transport Police confirmed "multiple casualties". Multiple people have suffered serious injuries.
Witnesses reported a vehicle hitting pedestrians and injured people on the ground.
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In a brief statement to USA Today, Williams said she isn't overly distraught by missing this event. "You know, she played well. First of all, the athlete referred to the baby as a " she ", so, yeah, Serena is definitely having a girl.
"A white van driver came speeding - probably about 50mph - veered of the road into the crowds of people who were walking along the pavement", she told BBC News. Jones said the van struck five or six people, and that she witnessed a man later being taken away in handcuffs.
One woman said she saw three people with what appeared to be their throats cut at London Bridge.
Simon Thompson told Sky News that he was just outside Borough Market when he saw crowds fleeing. "It looks potentially they could have been thrown over".
Others said they witnessed attacks in the market itself and a nearby restaurant, all of which are within a few minutes walk of the bridge.
Other eyewitnesses said three men came out of the van and started stabbing people at random with 12-inch knives close to the bridge, an area popular with tourists and citydwellers alike.
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The Labour leader faced tough questioning about his past alliances and views but remained calm and confident throughout. Questions that might have floored other politicians seemed to bounce straight off as he kept his composure throughout.