The high numbers of police officers on the streets will be "sustained" until further notice, the Home Secretary said today.
The number of officers patrolling the streets of London has almost trebled to 16,000 since last weekend to help tackle the violence.
Theresa May said that, despite the UK having had a trouble-free few nights, numbers would remain high.
Speaking during a visit to Enfield, north London, which was hit by rioters on Monday night, she said: "We will be sustaining the numbers for a period of time.
"We have had some quieter nights but we are not complacent about that.
"The police will maintain their tough arrest policy, their presence on the streets."
She said officers would be brought in from areas not affected by the riots to help maintain levels if necessary.
She met police and fire officers as she visited the Sony Distribution Centre in Enfield, which was destroyed by a blaze, believed to have been caused by looters.
Five people arrested in connection with the arson attack on the centre have been bailed, Scotland Yard said.
Leading companies such as XL and Domino - which are behind acts including Adele and Arctic Monkeys - are among those which used the destroyed distribution hub.
Mrs May said: "It is only by coming here and seeing the extent of the devastation that one can understand what was going on on the streets and the degree of criminality.
"What is key to us is that the police presence is there now, we are seeing arrests being made, and people being taken through the criminal justice system.
"The police will go after them (the criminals) relentlessly. If they were involved in this, the police will find them and they will be brought to justice."
During the visit, the Home Secretary paid tribute to police and fire officers who have helped tackle the riots across the country.
She said: "What I accept is that the people who got the riots under control were the brave policemen and women out there on the front line dealing with the riots as they were happening.
"I want to pay tribute, not just to our brave police officers but to the firefighters, who were also doing a fantastic job."
Nick de Bois, Conservative MP for Enfield North, agreed with the Home Secretary that high police numbers need to be maintained.
He said: "We need to keep a robust policing presence going, that's absolutely critical.
"I have met a lot of the police officers here and they have been working very, very hard.
"We need to keep the levels that we have got across London certainly beyond the weekend."
Mr de Bois said he witnessed the riots that broke out in Enfield town centre on Monday night.
He said: "I came down at 6pm before the riots started and I witnessed everything.
"I am absolutely convinced that two-thirds of them came from outside the borough. They were here to profit and to take on the police.
"They were criminals, they need to get the toughest sentences."
Smoke still billows from the remains of the Sony Distribution Centre and fire fighters continue to use water jets on the wreckage. Mr de Bois said: "What has happened here, at Sony, is devastating.
"But it's not just about the property, it's about over 200 people who work here. They are now worrying about their future.
"I want to get the Government with the council right behind ensuring Sony stay here to protect the jobs of people who work here."