"Our thoughts are with those who are caught up in these awful events".
A large number of police officers were seen gearing up with helmets and riot gear, believed to be on the hunt for suspects. Police say at least one person has been killed.
The two incidents are being described as terrorist attacks that were taken out in coordination.
A massive manhunt was launched after the incident.
United Kingdom police have killed or captured two suspects, with a massive search underway for the third. According to new reports, an eyewitness has reported a man entered an eatery in the Burrough Market and stabbed at least two people.
Borough Market, where the stabbing occurred, is a popular food market in south London, just south of London Bridge, with gourmet food and produce stalls and several restaurants inside. It hasn't been confirmed yet whether officers fired their weapons.
A third incident was also reported near Vauxhall.
Reporters for Reuters and The Spectator in London have confirmed that there is a heavy police presence on the bridge now, with more than 10 police vehicles present.
Ferrari have given Vettel preferential treatment, says Hamilton
Ferrari had a one, two finish has Sebastian Vettel edged out Kimi Raikkonen to win the Monaco Grand Prix on Sunday. I would like to think that at the end of the season those points are going to be valuable".
Soon after the incident, the BBC reported that police were looking for up to three armed men.
Authorities are also working a second incident at Borough Market, which is not far from London Bridge.
The incident happened on a warm Saturday night in a busy area full of bars and restaurants. One tweet read: "We need to be smart, vigilant and tough".
Witnesses reported seeing injured people on the ground on the bridge.
"A white van driver came speeding - probably about 50mph - veered off the road into the crowds of people who were walking along the pavement", she told BBC News. The witness said the van hit five to six people.
One witness said she saw three people with what appeared to be their throats cut on London Bridge.
Some netizens witnessed the incident tweeted that they saw people got injured and the police has come to deal with it. He said he threw chairs, glasses and bottles at the attackers in a bid to stop them.
In May 2017, a suicide bomber blew up in an Ariana Grande concert in Manchester, killing 23 adults and children. Britain has weathered two recent terrorism attacks in recent months. Several days later it was lowered to "severe", meaning an attack is highly likely.