The assault began Saturday night when a van veered off the road and barreled into pedestrians on busy London Bridge. Three men fled the van with large knives and attacked people at bars and restaurants in nearby Borough Market, police and witnesses said. The attack unfolded quickly, and police said officers shot and killed the three attackers within eight minutes.
Emergency officials said 48 people were treated at London hospitals, including some with life-threatening injuries, and a number of others suffered less serious injuries.
London police have arrested 12 people in east London in connection with London Bridge, Borough Market incidents.
It was the third attack in Britain in the past three months. Britain was already on edge after a suicide bombing two weeks ago at an Ariana Grande concert in Manchester, in northwest England, that killed 22 people and injured dozens of others. Grande and other stars are scheduled to perform a benefit concert for victims under tight security in Manchester Sunday night.
May, facing an election Thursday, said the recent attacks, including an earlier one outside Parliament in March, are not directly connected, but that "terrorism breeds terrorism" and attackers copy one another. She also said five credible plots have been disrupted since March.
"They are bound together by the single evil ideology of Islamist extremism that preaches hatred, sows division, and promotes sectarianism," she said. "It is an ideology that claims our W It was the third attack to hit Britain in as many months.
In March, a British convert to Islam ran down people with a vehicle on Westminster Bridge, killing four before fatally stabbing a policeman on Parliament's grounds.
Then came the May 22 Manchester concert bombing. After that attack, Britain's official terrorism threat level was raised from "severe" to "critical," meaning an attack may be imminent. Several days later it was lowered again to "severe," meaning an attack is highly likely.
May called on international communications companies to do more to block cyberspace to extremist groups who use it for recruitment and for encrypted information about plots.
She called for international agreements to regulate cyberspace and said Britain needs to become more robust at preventing the internet from being used to the advantage of extremist groups.
The British government has long sought more help from internet companies like Facebook and Google in the battle against extremism.
May spoke defiantly about protecting Britain's democracy - and vowed the election would go ahead as planned - after the violence turned a balmy summer night in an area packed with revelers into a scene of bloodshed and chaos, with officers running through crowded streets screaming for people to flee.
Boats on the River Thames helped evacuate the area, which is popular with tourists. It remained closed off Sunday as police urged residents and tourists to stay away.
May said the men attacked "innocent and unarmed civilians" in crowded Borough Market with blades and knives. She said they were wearing what appeared to be explosive vests, but police determined those were only meant to sow panic and fear.
Major parties suspended national campaigning Sunday out of respect for the victims, although the rightwing UK Independence Party said it would keep campaigning to show the extremists they couldn't sidetrack democracy.
May's Conservative Party had been expected to win by a wide margin but recent polls have showed the race tightening considerably. It is unclear how the unprecedented violence in the run-up to the election will impact voter sentiment.
Mayor Sadiq Khan said Londoners should remain vigilant but added: "I'm reassured we are one of the safest global cities in the world."
Khan said some of the injured were in critical condition. French and Spanish citizens were among the wounded.
Assistant Metropolitan Police Commissioner Mark Rowley said that while police believe all the attackers were killed, the investigation is expanding.
"We believe three people were involved, but we still have got some more inquiries to do to be 100 percent confident in that," he said.
As dawn broke over the capital, a large area on the south bank of the River Thames remained cordoned off. Police told people to avoid the area, leaving tourists and revelers struggling to get home. London Bridge and the adjacent train station, as well as nearby Borough subway station, were still closed.
Only hours before, bursts of gunfire echoed through the streets - likely from armed police - and at least three blasts rang out as officers performed controlled explosions after sweeping the area for possible bombs.
Witness Gerard Vowls told The Guardian newspaper that he saw a woman being stabbed by three men at the south end of London Bridge as the assault developed. He said he threw chairs, glasses and bottles at the attackers in a bid to stop them.
"They kept coming to try to stab me. They were stabbing everyone. Evil, evil people," he told the newspaper. "I want to know if this girl is still alive. I've been walking around for an hour and a half crying my eyes out. I don't know what to do."
Bartender Alex Martinez said he hid in a garbage bin for a half hour when a man stormed the nearly full restaurant where he worked.
"I saw that man with a knife in his hand and after that a man started screaming so I knew something wrong was happening," he said.
Medics treated the injured near the market as shocked people cried and shouted around them. Police officers yelled at people to run from the area.
Simon Thompson told Sky News that he was just outside Borough Market when he saw crowds fleeing.
"We ran for like 100 meters and then saw loads of police cars turned up and there was kind of a period of quite intense gunfire," he said. "I hid in a restaurant basement for about an hour. ... Police told us to get out and then there was more gunfire."
Police received the first call of reports of a vehicle hitting pedestrians on London Bridge at 10:08 p.m. (2108 GMT).
Soon after, reports started coming in of stabbings at Borough Market, a nearby area full of bars and restaurants surrounding a popular food market.
Photographer Gabriele Sciotto said he was on his way home from a pub when he saw a man running toward him telling him to turn around and run because there was an attack. As a documentary filmmaker, though, his instincts were to keep going.
The 25-year-old said that at first, "it didn't look too dangerous."
The men went into Borough Market, but then turned around and ran toward the Wheatsheaf Pub after being confronted by a police officer, he said, and suddenly a lot of police came from the other direction.
The attackers "had no clue what they were doing. They were scared. The police were scared," he said.
After one of the men was shot, Sciotto captured a photo of the suspect on the ground wearing what appeared to be canisters.
Police initially said officers were also responding to a third incident, in the Vauxhall neighborhood, but later said that turned out to be an unrelated stabbing.
Police tweeted a warning telling people in the area to run to safety, hide and then call police if it was safe to do so. They asked Londoners to "remain calm but be alert and vigilant."