Armed police and ambulances were called to reports of a white van hitting several people on London Bridge at 22:08 BST on Saturday.
The area and nearby railway stations were closed. Witness reports said the van mounted the pavement and swerved into a number of people.
BBC reporter Holly Jones, who was on the bridge, said: “A white van driver came speeding – probably about 50mph – veered off the road into the crowds of people who were walking along the pavement.
“He swerved right round me and then hit about five or six people.”
The vehicle continued to drive to nearby Borough Market, where the suspects stabbed several people in an area crowded with people having an evening out.
The Metropolitan Police confirmed six people had died and 48 required hospital treatment. In addition, three suspected attackers were shot dead.
British Transport Police said one of its officers was seriously injured responding to the attack.
A third police unit was sent to the Vauxhall area. Officers later said this was a stabbing and not connected to the operation at London Bridge and Borough Market.
London Ambulance Service took more than 100 emergency calls about the attack.
The Metropolitan Police said six people died in the attack.
London Ambulance Service said it had taken 48 people to five different London hospitals.
The “seriously injured” British Transport Police officer suffered head, face and leg wounds.
Meanwhile, people described as “walking wounded” were moved to the Andaz Hotel at Liverpool Street where there were paramedics and more armed police.
Police boats also searched the River Thames for anyone who may have fallen from the bridge.
The Metropolitan Police has opened its Casualty Bureau for people concerned about friends or relatives. No victims have yet been named.
Three men, believed to be the attackers, have been shot by police.
Police said the men were shot within eight minutes of officers receiving the first reports of the attack.
Witnesses had described seeing between two and four men getting out of the van after it crashed south of London Bridge.
Police confirmed shots were fired at Borough Market and a photographer took a picture showing two people lying on the ground outside the Wheatsheaf pub.
One of the people on the ground appears to have canisters strapped around his waist, and police said the men were wearing hoax explosive vests.
The person who took the photo said he saw three people shot by police.
What is currently happening?
The investigation is being led by the Counter Terrorism Command.
London Bridge is completely closed and will remain so, British Transport Police said.
Police believe they may have caught all the attackers but armed officers continue to sweep the area.
A casualty line has been set up for members of the public who are concerned about friends and relatives. People have been told they can ring 0800 096 1233 or 020 7158 0197 but only “in a genuine emergency”.
London Bridge and Borough stations have been closed and trains are passing straight through.
Network Rail also said Waterloo East, Charing Cross and Cannon Street stations were closed and there were delays at Blackfriars.
The River Thames has been reopened to boats.
Nearby Guy’s Hospital has been placed in lockdown as a precaution to keep staff and patients safe, as have St Thomas’ and the Evelina Children’s Hospital a mile away.
Police have been clearing streets, bars and restaurants around Borough Market, a very busy area of the capital especially on Saturday nights.
Pentecost services at Southwark Cathedral have been cancelled as the cathedral is within the police cordon.
Prime Minister Theresa May and Mayor of London Sadiq Khan both said they are being kept “regularly updated” on events.
Mrs May said: “Our thoughts are with those who are caught up in these dreadful events.”
The prime minister will chair a meeting of the government’s Cobra emergency committee on Sunday, which Mr Khan will attend.
Mr Khan described the events as a “deliberate and cowardly attack on innocent Londoners and visitors to our city enjoying their Saturday night”.
Labour leader Jeremy Corbyn called the attack “brutal and shocking”.
Lib Dem leader Tim Farron said it was a “horrific incident” and Scotland’s First Minister Nicola Sturgeon called it “dreadful news”.
The US State Department said it “condemns the cowardly attacks targeting innocent civilians in London”.
French President Emmanuel Macron said his country “is more than ever at the side of the United Kingdom”.
Residents and businesses in the area have been offering shelter to people. The hashtag #SofaForLondon has been used to share offers.