One witness told the BBC a white van veered off the road and struck as many as six people.
"From 2208 hrs (local time) officers responded to reports of a vehicle in collision with pedestrians on #London Bridge".
Incident 3 - London police say they are now responding to incident in Vauxhall area.More news: Cavs Beat Celtics As LeBron James Tops NBA's All-Time Playoff Scoring List
"This is a fast-moving investigation".
Labour leader Jeremy Corbyn called the news "brutal and shocking" in a tweet.
It is too early to say whether the incidents in London are militant attacks, European security officials told Reuters."It's too soon to say" if London Bridge incident is an attack by militants, one official said.
"He swerved right around me", Jones said, "and then hit about five or six people".
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.
Witnesses reported seeing injured people on the ground on the bridge. "They all have paramedics assisting them at the moment".
United Kingdom television showed police leading dozens of people down city streets with their hands on their heads.More news: Ariana Grande Vows Return To Manchester In Letter To Fans
Police have so far been scant with details, saying they will release information when they can.
Latest reports claim police are looking for three suspects, possibly armed.
The Telegraph has reported that a van injured as many as 15-20 people, according to witnesses, but these numbers are not confirmed. "It is still unfolding", Ms Bishop said. The BBC showed dozens of people, evidently having been caught up in the attack, being escorted through a police cordon with their hands on their heads. "Some of them were coming by auto, some of them were running".
"We were in an Uber (taxi) going towards London Bridge and suddenly we saw people running".
"He looked in a bad way".
"After that I heard what sounded like gunfire from Borough Market".
He added: "I feel sick". "The police came pretty quickly".More news: MTV will livestream Sunday's Manchester benefit concert
"There was rapid fire because that's why I thought it was fireworks".