Saturday night's atrocity in the capital was the third terrorist outrage to hit the country this year. Three suspected terrorists were killed and a dozen arrests have been made.
The prime minister said that, although there was no connection between Saturday's attack and the suicide bombing at Manchester Arena two weeks ago, Britain was facing a new wave of low-tech, copycat attacks.
May called on worldwide communications companies to do more to block cyberspace to extremist groups who use it for recruitment and for encrypted information about plots.
"And at the same time the security and intelligence agencies and police have disrupted five credible plots since the Westminster attack in March".
"In terms of their planning and execution, the recent attacks are not connected but we believe we are experiencing a new trend in the threat we face".
The attack in central London came just weeks after a suicide bombing at a concert in Manchester left 22 dead, and it recalled an attack in March when a man drove a vehicle into pedestrians near the seat of Parliament, killing five. "People running everywhere, police shouting to run away".
"There was a auto with a loudspeaker saying "go, go" and they (police) threw a grenade. and then I ran", he said.
The attack in central London came just weeks after a suicide bombing at a concert in Manchester left 22 dead, and it recalled an attack in March when a man drove a vehicle into pedestrians near the seat of Parliament, killing five. Mrs May said they were "worn only to spread panic and fear".
Mrs May said the United Kingdom has made "significant progress" in disrupting plots and protecting the public since the emergence of the threat from Islamist-inspired terrorism. She said she has worked in Brick Lane - an area famous for being home to successive waves of immigrants over the centuries - since 1953.
"They want their violence to overwhelm our right to vote in a fair and peaceful election and to go about our lives freely". Our society should continue to function in accordance with our values.
Major parties suspended national campaigning Sunday out of respect for the victims, although the right-wing UK Independence Party said it would keep campaigning to show the extremists they couldn't sidetrack democracy.
"As a country, our response must be as it has always been when we have been confronted by violence".
"We must come together, we must pull together, and united we will take on and defeat our enemies".
After a militant attack on a nightlife district of London this weekend, British Prime Minister Theresa May will resume campaigning on Monday just three days before a national election which polls show is much tighter than previously predicted.
Emergency officials said 48 people, including a transport police officer and an off-duty officer, were treated at hospitals across London.
"However, the police will ensure appropriate protective security measures are implemented".
Scotland Yard head Cressida Dick disclosed that police believe there were three attackers and that all had been "neutralised".
A large cordon remains in place in the affected areas as officers conduct searches to ensure there are no suspects outstanding.
Meanwhile, Australia's foreign minister Julie Bishop says three Australians have been injured in the knife attacks at London Bridge and in London's Borough Market.
The Met Police commissioner declined to give any details about the identities of the attackers at this stage.
She also had praise for the emergency services, adding: "Last night we saw yet again the bravery, dedic- ation, selflessness and professionalism of the police and of those who work in the NHS and fire service".
Witnesses said the terrorists drove into pedestrians on the bridge in the same way as Westminster Bridge attacker Khalid Masood.
Several people said they were ordered by the police to stay inside pubs and restaurants as the terror raged outside.
Morrison said in a video: "All of a sudden this guy comes up with a knife". Terrorists are using cars and knives, as they did Saturday night and in the March attack outside Parliament, which are harder to pick up in advance than explosives. Then he came in and walked around the restaurant.
"I chucked it, but I think I missed one of them, and then I picked up a stool, and I threw it at him".