Parliament will return to duty on Thursday, as the political fallout from the rampage takes hold. The crisis is a major test for Cameron's Conservative-led coalition government.
Other politicians visited riot sites Tuesday — but for many residents it was too little, too late.
Deputy Prime Minister Nick Clegg was booed by crowds who shouted "Go home!" in Birmingham, while London Mayor Boris Johnson — who flew back overnight from his summer vacation — was heckled on a shattered shopping street in Clapham, south London.
Johnson said the riots would not stop London from "welcoming the world to our city" for the Olympics.
"We have time in the next 12 months to rebuild, to repair the damage that has been done," he said. "I'm not saying it will be done overnight, but this is what we are going to do."
Violence first broke out late Saturday in the low-income, multiethnic district of Tottenham in north London, after a protest against the fatal police shooting of Mark Duggan, a 29-year-old father of four who was gunned down in disputed circumstances Thursday.
Police said Duggan was shot dead when officers from Operation Trident — the unit that investigates gun crime in the black community — stopped a cab he was riding in.
The Independent Police Complaints Commission, which is investigating the shooting, said a "non-police firearm" was recovered at the scene, but that there was no evidence it had been fired — a revelation that could fuel the anger of the local community.
An inquest into Duggan's death was opened Tuesday, though it will likely be several months before a full hearing.
Duggan's death stirred memories of the 1980s, when many black Londoners felt they were disproportionately stopped and searched by police. The frustration erupted in violent riots in 1985.
Relations have improved since then but tensions remain, and many young people of all races mistrust the police.
Others pointed to rising social tensions in Britain as the government slashes 80 billion pounds ($130 billion) from public spending by 2015 to reduce the huge deficit, swollen after the country spent billions bailing out its foundering banks.
Many rioters appeared to relish the opportunity for violence Monday night. "Come join the fun!" shouted one youth as looters hit the east London suburb of Hackney.
In Hackney, one of the boroughs hosting next year's Olympics, hundreds of youths left a trail of burning trash and shattered glass. Looters ransacked a convenience store, filling plastic shopping bags with alcohol, cigarettes, candy and toilet paper.
In Croydon, fire gutted a 140-year-old family run department store, House of Reeves, and forced nearby homes to be evacuated.
"I'm the fifth generation to run this place," said owner Graham Reeves, 52. "I have two daughters. They would have been the sixth.
"No one's stolen anything," he said. "They just burnt it down."
On Tuesday, as Londoners emerged with brooms to help sweep the streets of broken glass, many called for police to use water cannons, tear gas or rubber bullets to disperse rioters, or bring out the military for support. Although security forces in Northern Ireland regularly use all those methods, they have not been seen on the mainland in decades.
Conservative lawmaker Patrick Mercer said that policy should be reconsidered.