British media reported that more than one person had been killed in the rampage.
In a statement afterwards, she said recent terrorist attacks in the United Kingdom were not linked by a common network but by an extremist ideology.
A massive manhunt was launched after the incident.
Armed police were also reportedly spotted outside the Andaz Hotel in Liverpool Street, where the walking wounded were reportedly taken.
The suspects are then believed to have exited the van and proceeded on foot towards the nearby area of Borough Market, one of the capital's most popular nightlife spots.
"The terrorists were confronted and shot by armed officers within eight minutes of the police receiving the first emergency call".
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.
Witnesses report a van hitting pedestrians and injured people on the ground. Officers have then responded to reports of stabbings in #BoroughMarket.
The attackers were shot dead by police.
"Officers are now responding to an incident in the #Vauxhall area", the statement added.
"We need the Travel Ban as an extra level of safety!" he said in the other.
(AP Photo/Matt Dunham) Police vehicles in a street near London Bridge during the ongoing terrorist incidents at London Bridge and Borough Market.
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Three men then left the vehicle and stabbed a number of people in Borough Market, south of the bridge, an area known for its restaurants and bars.
Armed British police officers walk within a cordoned off area after an attack in the London Bridge area in London, Sunday, June 4, 2017.
A married couple, Natalie and Ben, said they saw a man with "quite a large blade. maybe 10 inches".
"It is important for the public to work with us and remain vigilant as we tackle the on-going terrorist threat".
Another witness claimed that one of the suspects at Borough Market was carrying a "massive knife" as he entered a cafe and stabbed two people inside.
Tim Farron, the Lib Dem leader, said: "Tonight's horrific incidents in London remind us how much we owe our emergency services".
She explained: "Shortly before 10 past 10 yesterday evening, the Metropolitan Police received reports that a white van had struck pedestrians on London Bridge".
"Within my line of sight, there were five or six people on the ground that were not moving", he said.
"A man suddenly appeared in the restaurant with a massive knife - some people in the restaurant believe there may have been another man - but it was so chaotic it was hard to tell", the witness said.
Some of the 48 people injured are in a "critical" condition, London Mayor Sadiq Khan told reporters Sunday in comments broadcast by the BBC.
Witnesses said people ran into a bar to seek shelter.
Police specialists collected evidence in the heart of London after a series of attacks described as terrorism killed seven people and injured more than 48 others.
"As terrorism breeds terrorism and perpetrators are inspired to attack, not only on the basis of carefully constructed plots after years of planning and training, and not even as lone attackers radicalised online, but by copying one another and often using the crudest of means of attack".