More than one person was killed when a van mowed down pedestrians on London Bridge late on Saturday, British police said.
The capital's Metropolitan Police said they were also responding to stabbings in Borough Market, not far from the bridge, and in Vauxhaul area, located on the south side of the city, Efe reported.
The Met said in a tweet that officers had also been deployed to deal with an incident in Vauxhall.
Prime Minister Theresa May said that she has been following updates from police and security officials, and she could confirm that the incident in London was being treated as a potential act of terrorism.
"This is a fast moving investigation. I want to express my huge gratitude to the police and emergency services who are on the scene. Our thoughts are with those who are caught up in these dreadful events," May said.
Police in the British capital said that a deadly collision of a van with pedestrians on London Bridge and a subsequent stabbing at a restaurant in the vicinity were acts of terrorism.
"(T)he incidents at #LondonBridge & #BoroughMarket were declared as terrorist incidents," the London Metropolitan Police said on Twitter, minutes after Prime Minister Theresa May said her government was treating the case as a "potential act of terrorism."
Saturday night's "terrible incident" will be the focus of a meeting of the UK government's Cobra emergency committee, May's office said.
While categorising the events at London Bridge and Borough Market as terrorism, the Met said that a third incident, in the Vauxhall area, had been determined to have no connection to what happened at the other locations.
According to a report in the BBC, transport for London said London bridge has been closed in both directions due to a "major police incident". Bus routes were being diverted and the neighbouring Southwark Bridge has also been shut.
No-one has so far claimed responsibility for the terror attacks in central London.
BBC reporter Holly Jones, who was on London bridge, said the van was driven by a man and was "probably travelling at about 50 miles an hour".
"He swerved right round me and then hit about five or six people. He hit about two people in front of me and then three behind," Jones was quoted as saying.
Another married couple who happened to witness the incident on London Bridghe said: "We saw a man in red with quite a large blade, we don't know the measurement, maybe 10 inches. He was stabbing a man...he stabbed him about three times fairly calmly."
Social media giant Facebook has activated its safety check feature for what it is calling "The Attack in London, United Kingdom".
Responding to the London incidents, US President Donald Trump sent out a series of tweets assured the British people that his country will do whatever to help the people in London.
"Whatever the United States can do to help out in London and the U. K., we will be there - WE ARE WITH YOU. GOD BLESS!" Trump tweeted.
"We need to be smart, vigilant and tough. We need the courts to give us back our rights. We need the Travel Ban as an extra level of safety!" he added.
The incidents in London come less than two weeks after 22 people were killed in the northern city of Manchester when a suicide-bomber detonated explosives as fans were leaving a concert by pop singer Ariana Grande.
In the wake of the Manchester attack, the UK government increased the terror alert to critical, the highest level, and deployed the army to support police.