The prime minister has said "it is time to say enough is enough" as she condemned a terror attack on "innocent and unarmed civilians" which left seven people dead and 48 injured in London.
A white van hit pedestrians on London Bridge at about 22:00 BST on Saturday, then three men got out and stabbed people in nearby Borough Market.
The three attackers, who wore fake bomb vests, were shot dead by police.
Mrs May said the UK's counter-terrorism strategy would be reviewed.
It is the third terror attack in the UK in three months, following the car and knife attack in Westminster in March, which left five people dead, and the Manchester bombing less than two weeks ago, in which 22 people were killed.
Most political parties have suspended national general election campaigning, but UKIP leader Paul Nuttall said he would not follow suit because that was "precisely what extremists would want us to do".
Mrs May said full campaigning would resume on Monday and the general election would go ahead as planned on Thursday.
Eyewitnesses to the attack described seeing a white van travelling at high speed along London Bridge, hitting pedestrians, before crashing close to the Barrowboy and Banker pub.
BBC reporter Holly Jones, who was on the bridge, said the van was "probably travelling at about 50 miles an hour" and hit "five or six people".
Three men then got out and began attacking people in the nearby market - an area known for its bars and restaurants which were busy on a warm summer evening.
Terrified drinkers rushed away from the scene, some taking shelter in London Bridge Underground station.
One witness, Gerard, told the BBC he saw one woman being stabbed "10 or 15 times" by men shouting "This is for Allah".
Another, Eric, told the BBC the men "ran towards the people that they nearly ran over".
"I thought, 'Oh maybe they're worried about them and trying to comfort them...
"[Then] they literally just started kicking them, punching them, they took out knives... it was a rampage really."
The three suspects were shot dead within eight minutes of the first 999 call being received.
Metropolitan Police Commissioner Cressida Dick praised the "extraordinary bravery" of her officers, on and off duty, who risked their lives by rushing to confront the attackers.
She said she understood there could be a certain amount of "fear" among Londoners, but added: "The last thing we need is people over-reacting or taking out their frustrations on people in other communities or in their own communities."
Among the main developments:
■ More than 80 medics were sent to the scene. The injured, some of them in critical condition, are being treated in five London hospitals
■ The Met Police has set up a casualty bureau on 0800 096 1233 and 020 7158 0197 for people concerned about friends or relatives
■ Two Australian citizens "have been directly impacted," says the country's Prime Minister Malcolm Turnbull
■ Four French citizens have been injured, one seriously, according to foreign minister Jean-Yves Le Drian
Another eyewitness, Steven Gibbs, who was drinking in St Christopher's Inn, just metres from the scene, told the BBC: "A black cab drove past and the driver shouted, 'Terrorist attack, run!'
"I stood up to take a look and then all of a sudden there were gunshots. Lots of people were screaming."
Steven was taken into the basement of the bar before the police came in and told everyone inside to run.
"I've never been so scared in my life," he said.
At the scene: Cherry Wilson, BBC News website
No-one has been able to clean up the empty pint glasses on the tables outside Belushi's bar on Borough High Street - a stark reminder of what happened in London Bridge last night.
It's 8am and dozens of police cars and cordons remain in the area, blocking anyone from walking up to Borough Market, where the tragedy unfolded.
Dozens of people wait by the police cut-off areas in a confused state trying to work out how to get home or to work.
But no-one is prepared to give up.
There is a determined resilience in the air with nurses and railway workers walking miles out of their way to try to get to their jobs.
Security officer Mohammed Osman, who works on Borough High Street, had to wait for an hour before he was allowed through to his place of work.
He said: "I'm not feeling worried. I'm strong enough. These enemies are trying to divide us but we have to be together."
London Mayor Sadiq Khan said the capital remained the "safest global city" and would not be cowed by terrorism.
Neil Coyle, the Labour candidate for Bermondsey and Old Southwark, praised the "amazing" response of Londoners.
"The cabbies who offered free rides, the hotels offering accommodation and people just offering a spare room, a sofa for the evening or somewhere just to charge a mobile phone, to make sure that those directly affected could keep in touch with their families and loved ones."
The police are asking anyone with photographs or videos of the incident to upload them here.
The area around the attack scene remains cordoned off on Sunday morning, with London Bridge closed. Neighbouring Southwark Bridge has now reopened.
Many other roads, including Borough High Street and Lower Thames Street, are also closed, and trains are not stopping at London Bridge rail station or Tube station.
Terrorism begins to feel like the new normal
Analysis by Dominic Casciani, home affairs correspondent
With three attacks in close proximity, terrorism against soft targets is beginning to feel, to some people, like the new normal.
The brutal reality is that this kind of threat is absolutely typical of what jihadists sought to achieve in all their attacks across Europe.
Since 2013 security services in the UK have foiled 18 plots. A large proportion of those have involved suspects who set out to commit acts of violence similar to the attack on Westminster Bridge and London Bridge.
Plans to use bombs, such as at Manchester Arena, are rarer because plotters need to have the technical skills for such an appalling attack - but attacking people with cars and knives is far easier and has long been encouraged by so-called Islamic State and other jihadists.
The aim of the three attackers last night is abundantly clear - not only did they want to kill, but they almost wanted to lose their own lives.
They would've known full well that attacking people in the street would draw armed police in their direction and the fake bomb belts they were wearing would, in their own warped minds, hasten their demise.
BBC