LONDON -- Terrorism struck at the heart of London, police said Sunday, after a vehicle veered off the road and mowed down pedestrians on London Bridge and witnesses told of men with large knives stabbing passersby at nearby Borough Market.

Police said six people died and 20 were injured in the attacks, while police shot dead three suspects. The Metropolitan Police head of counter-terrorism, Mark Rowley, said police believe all of the attackers were killed, but investigations are underway to ensure there are no more.

The violence turned a summery Saturday night in an area packed with bars and restaurants into a scene of panic and chaos, with officers running through crowded streets screaming for people to flee and lifeboats drafted to help clear the area.

The Metropolitan Police force declared the attacks "terrorist incidents."

Hours after the attacks began, a large area of central London remained cordoned off and police told people to avoid the area, leaving tourists and revelers struggling to get home. It was unclear whether any of the attackers was on the run.

Bursts of gunfire echoed through the streets -- likely from armed police -- and at least three blasts rang out as police performed controlled explosions. One image taken by a witness showed a man on the ground surrounded by police; he appeared to be wearing a vest with canisters attached to it.

Gerard Vowls told The Guardian newspaper that he saw a woman being stabbed by three men at the south end of London Bridge. 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 restaurant where he worked, which was nearly full.

"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 metres 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."

The mayhem began just after 10 p.m. (2100GMT), when police responded to reports of a vehicle hitting pedestrians on London Bridge, which crosses the River Thames in central London. Multiple witnesses reported a vehicle veering off the road and hitting as many as six pedestrians.

"We saw injured people on the road, injured people on the pavement," witness Will Heaven told Sky News.

Soon after, reports started coming in of stabbings at Borough Market, a nearby area full of bars and restaurants surrounding a popular food market. Witnesses reported seeing as many as three attackers with knives.

Police initially said officers were also responding to a third incident, in the Vauxhall neighbourhood, 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 is safe to do so. They asked Londoners to "remain calm but be alert and vigilant."

Prime Minister Theresa May confirmed the attack "is being treated as a potential act of terrorism" and said her thoughts were with "those who are caught up in these dreadful events." May's office said she would chair a meeting of the government's COBRA emergency committee on Sunday.

As thousands of people flooded from the area of the attacks -- many unable to get home with nearby subway stations shut -- locals were quick to offer assistance.

The Royal Oak pub, near the area of the attacks, opened its doors to people evacuated from hotels. At least one taxi company offered free rides to people stranded in the area. Phaldip Singh, who describes himself as an entrepreneur and youth activist, tweeted that Sikh temples were open to provide food and shelter for those affected.

If confirmed as terrorism, this would be 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, then stabbed a policeman to death outside Parliament.

On May 22, a British suicide bomber killed 22 people and injured dozens at an Ariana Grande concert in Manchester. After that attack, Britain's official threat level from terrorism was raised to "critical," meaning an attack may be imminent. Several days later it was lowered to "severe," meaning an attack is highly likely.

A charity concert for victims of the Manchester attack, featuring Grande and other stars, is due to be held in the northwest English city on Sunday.

Niko Price in London contributed to this story.