The three attackers were shot dead by police within minutes.
Dick said police believed that the incident was under control, but a large police cordon remained in place in the area, south of the Thames, Sunday.
She added that police patrols will be increased in London, including those by armed officers.
***
09:38
Six people have been killed in a terror attack in central London in which three assailants were shot dead by police, Scotland Yard has said.
A white van hit several pedestrians on London Bridge at about 22:00 BST before apparently crashing into railings.
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 officers confronted and shot the suspects within eight minutes.
London Ambulance Service said 48 people have been taken to five hospitals. More than 80 medics were sent to the scene to help those hurt.
One of the injured is an officer from British Transport Police who was stabbed after responding to the incident. His condition is serious, but not life-threatening.
Metropolitan Police Assistant Commissioner Mark Rowley said: "The suspects were wearing what looked like explosive vests but these were later established to be hoaxes."
He said it was currently believed there were only three attackers involved.
"We are treating this as a terrorist incident and a full investigation is already under way," he added.
The incident 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.
Prime Minister Theresa May described Saturday night's as "dreadful" and will chair a meeting of the government's Cobra emergency committee later.
London Mayor Sadiq Khan called it "a deliberate and cowardly attack on innocent Londoners".
'Van swerved'
BBC reporter Holly Jones, who was on the bridge at the time of the attack, said the van was "probably travelling at about 50 miles an hour".
"He swerved right round me and then hit about five or six people. He hit about two people in front of me and then three behind," Ms Jones told the BBC News Channel.
Eyewitnesses said they saw people getting out of the van after the attack on the bridge and running towards Borough Market.
A security guard who oversees a number of pubs in the London Bridge area told the BBC he saw four people stabbed by three attackers.
Gunshots were later heard in the area while one social media user posted a photograph appearing to show one of the attackers lying on the ground outside a pub in the food market, with what police now say was a fake bomb vest strapped to his body.
Eye witness Will Orton described being in a pub in the area and seeing people coming running inside.
"We didn't really know what was going on," he said.
"We thought maybe there was a fight or something outside. And then there were almost hundreds of people coming inside.
"The bouncers did a really good job, they shut the doors and locked everyone in. There was panic - it seemed like it was literally outside the door. People were coming inside and saying they had witnessed people being stabbed."
On Twitter, Labour Party leader Jeremy Corbyn described the incidents as "brutal and shocking".
Transport for London (TfL) said London Bridge had been closed in both directions, while neighbouring Southwark Bridge has also been shut.
TfL said there were further closures in Borough High Street, while on the north side of the river, road closures included Lower Thames Street.
The Met Police has set up a casualty bureau on 0800 096 1233 and 020 7158 0197 for people concerned about friends or relatives who may be affected.
Facebook has activated its safety check so people in London could post a message to let friends and relatives know they were safe.
The police are asking anyone with photographs or videos of the incident to upload them here.
More about: #Londonattack
