Several witnesses said some victims also appeared to have stab wounds.
London authorities are investigating reports that a vehicle has hit pedestrians on London Bridge.
"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.
London Ambulance Service said: "We can confirm we have taken at least 20 patients to six hospitals across London following the incident at London Bridge".
Eyewitnesses told BBC home affairs correspondent Tom Symonds they saw people getting out of the van after the attack on the bridge and running towards Borough Market.More news: Man Utd cool interest in Griezmann
Heaven said he saw armed police arriving on the scene.
Here's all that happened on the night of Saturday that caused chaos on the streets of London.
UK PM Theresa May has called the events a "terrible incident" that is being treated as a "potential act of terrorism".
"It's just hard being over here in the states, because we live here now and looking on the news with the things back home, there's nothing we can do. We need the Travel Ban as an extra level of safety!" he added.
In this image made from PA Video footage, people receive medical attention in Thrale Street near London Bridge following a terrorist incident.
British Transport Police said they have received reports of multiple casualties. Reuters television pictures showed dozens of emergency vehicles in the area around London Bridge. "We are with you", he tweeted.More news: No sign of the ultimate deal as Donald Trump leaves Israel
'So until we know otherwise we can assume that this does follow a similar pattern to those we have seen elsewhere'.
More recently, a suicide bomber killed 22 people at a music concert by US pop singer Ariana Grande in Manchester on May 22.
Nick Archer, who was in the London Bridge area, says he came out of a bar and looked to his left and saw a man lying on the ground.
Attacker Khalid Masood first drove his auto at pedestrians on the pavement on Westminster Bridge before crashing into a perimeter fence.
London Mayor Sadiq Khan called the attack "barbaric".
Around 22:00 BST (British Standard Time), a white van ran onto at least 30 people on the bridge and three men who got out of it started to assail people with knife.More news: Police at London Bridge after car reportedly plows into people
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