London police report "incident" on London Bridge. "The suspects were wearing what looked like explosive vests but these were later established to be hoaxes", he said.
According to some unconfirmed reports, ISIS has taken responsibility for the attack.
Mark Rowley, assistant commissioner of London's Metropolitan Police Service, said the attackers were shot and killed by police.
At least six people were killed by attackers near London Bridge on Saturday, police said.
Italian photographer Gabriele Sciotto, who was watching the Champions League final at the Wheatsheaf pub in Borough Market, said he saw three men shot just outside the pub. BBC showed dozens of people, evidently caught up in the attack, being escorted through a police cordon with their hands on their heads.
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"Everyone in the bar started pushing people from the exits", one witness who gave his name as Brian, 32, told Reuters. Witnesses reported seeing as many as three attackers with knives. The other was a multiple stabbing at nearby Borough Market, a gourmet food market with several restaurants that would have been busy with diners and drinkers on a Saturday night.
"One of them had a big knife, then he came in and walked around the restaurant, I guess they just kind of stabbed anyone that they saw and knocked things on the ground and then we just hid".
Police said they responded to the incident on London bridge at 2208 (2108 GMT).
He told the station: "I didn't see the van mount the kerb but I saw everything else". Witnesses said they heard gunfire in the area. Britain has weathered two terrorism attacks in recent months. More than 30 injured people were taken to hospital.
The first report was of a van ploughing into pedestrians on London Bridge.