Officers fired shots, although authorities declined to provide additional information on the reported attack.
However, Vauxhall Station has reopened and it is believed the incident there was an unrelated stabbing.
The attack began at about 10.30 p.m. local time. The condition of the stabbed people was not known.
A witness told Reuters she saw people with apparent knife wounds on the bridge. Jones said the van struck five or six people, and that she witnessed a man later being taken away in handcuffs.
Six people have died and many more injured in terror attacks using a van and knives on Saturday night.
"Then we heard three gunshots, definitely gunshots, and we ran".
He said: "I thought at first it was fireworks then I recognised it was significant gunfire and that was the first instance". At that point, I ran towards them. They reportedly attacked pedestrians on the street, and stormed into a nearby restaurant, attacking patrons and staff.
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I went to our house and knocked on the door. "If you raped three, I will own up to it". He later apologised and said he did not intend to disrespect women or rape victims.
There are unconfirmed witness reports from the scene at London Bridge tonight that people may have been stabbed.
"Then we hid under the table and people came into the restaurant and knocked a bunch of stuff over, like the till".
Rowley said more than 20 other people were injured and hospitalized. She witnessed the injured being treated by paramedics, she said.
Police activity spread throughout the Borough Market area. "One of the officers jumped out and started attending to the guy on the floor".
She said police were firing weapons.
Armed police are at the scene of the apparent attack, along with helicopters and ambulances.
Police are urging the public to remain calm, be alert and stay vigilant. "We were eventually led out of the bar and some kind people working in a hotel let us come in to use the bathroom and to give us water".
Trump tweeted "we are with you" and said the United States would do whatever was needed to help.
Police have also responded to an incident at Borough Market, which is within half a mile of the London Bridge, and Vauxhall, which is three miles away.