Mr Johnson, who flew back from his summer holiday yesterday as the violence escalated across the capital, said: "I want to say to everybody who runs a shop or owns a business here how very sorry I am for the loss and the damage you have suffered.
"I also want to say to the people who have been involved in instigating these riots and those who have been robbing and stealing that they will be caught, they will be apprehended and they will face punishments they will bitterly regret. They will.
"I know there are questions about the police response and police numbers. We are certainly going to be dealing with those."
Mrs May was led away by aides as a visibly-stunned Mr Johnson faced the television cameras and public wrath.
One woman told him: "I was in a salon when a brick came through the window and no one was here to defend me."
Another woman shouted at the mayor, urging him to resign.
Mr Johnson struggled to make himself heard as he said: "Tonight we are going to have a huge number of police on the streets."
He added: "It is time that people who are engaged in looting and violence stopped hearing economic and social justification for what happened."
The mayor, who was eventually guided away from the crowds and television cameras, followed other leaders by ending his stay abroad to join efforts to quell the violence that has blighted London.
The move came despite Mr Johnson's aides previously insisting he could deal with the burgeoning crisis remotely as if "he was sitting in his office".
Mr Johnson arrived at a cordon outside Clapham Junction station where members of the public gathered.
He was to greeted by the sight of a burnt-out fancy dress shop being hosed down by firefighters, surrounded by litter strewn on the streets and smashed windows.
Crowds of people armed with brooms waited for permission to enter the cordon, which covered St John's Hill and Lavender Hill, to start a clean-up operation - a movement started on Twitter.
The mayor walked the length of devastated streets, past window after window of shops that were smashed in the riots last night.
Mr Johnson received a mixed reaction veering from almost carnival spirit to anger and rage.
He managed to turn ill-feeling to positive at one point by taking hold of a broom and thanking crowds for turning out.
Mr Johnson paid tribute to the army of volunteers hoping to sweep Clapham's streets.
He said: "Thank you very much to everybody who has come here to clear up the mess.
"That is the spirit of London."
When asked by one angry resident why he had not come home from his holiday earlier, the mayor replied: "I came as fast as I could."
He said police had been overstretched but that same situation would not happen again.
Mr Johnson told the crowd: "It's time we heard a little bit less about the sociological justifications for what is in my view nothing less than wanton criminality.
"In the meantime I want to thank you all for coming along here today.
"I know you've been waiting for a long time to come and sweep up the streets."
He told waiting media: "I do not want to see a repetition of the events of last night.
"It's time for London and the majority of innocent law-abiding Londoners to reclaim their streets.
"In 2012, next year, we are going to be welcoming the world to our city and it's a great city, it's a peaceful and fundamentally safe city and when they come they will find one of the safest big cities.
"We have time in the next 12 months to rebuild, to repair the damage that has been done, to rebuild these buildings that have been destroyed.
"I'm not saying it will be done overnight, but this is what we are going to do."
The mayor blamed the situation on a "mental contagion" taking over youths' minds.
"And when it does stop they will regret bitterly what they have done."
But Mr Johnson's presence was not positive for everyone.
One elderly woman from Battersea, who would only give her name as Brenda, said she was frustrated she had not been able to hear much of what the mayor said as he had not used a megaphone.
She also said she was frustrated he spent time facing the press, rather than concentrating on people gathered to meet him.
"I desperately wanted to speak to him but I couldn't hear him," she said.
"In this day and age, he could have had a megaphone.
"He should have been prepared.
"I said to him, 'if you can't be prepared for that, how can you be prepared for all this other stuff?'."
She described confronting youths in Clapham last night as they put masks on preparing for trouble.
"I saw one group and told the community support officers about them.
"Then I saw another group and asked, 'why don't you go to the cinema?'
"They just said: 'there's nothing on!"'
Leon Fearon, 19, from Lewisham, said the mayor had not listened to the voice of young people.
"Boris needs to concentrate on what people are saying to him," he said.
"Youths don't have the minds that politicians have, they are running around stealing from shops but what else do they have?
"I'm not condoning them but someone needs to listen to them.
"They are not getting their point across in the right manner, but they need to have a way of saying something."
Home Secretary Theresa May, during the same visit to Clapham as Mr Johnson, said: "This is pure criminality, all this looting, thieving and rioting.
"What we are doing tonight is putting on double the number of police, but crucially we are arresting the people who are perpetrating crime."
She said those who had committed crimes would be identified using CCTV images which will be released, and then brought to justice.
Sarah Hutchings, 45, and sister Kelly Hutchings, 42, among the crowds joining the clean-up operation, saved their criticism for parents of those involved in the violence.
Painter and decorator Kelly Hutchings, who lives in Clapham, said: "There were about 70 kids running down the street at about 1.45am.
"They set fire to my old neighbour's Mini outside my house. There's soot from it all in my front room.
"I walked down Battersea Rise and all down everything has been smashed and robbed, even charity shops.
"I blame the parents in some ways. I phoned a friend at about 2.15am to tell her I could see her 14-year-old son outside my house. She said 'You've just woke me up'!"
Sister Sarah, who lives in west London, said she grew up in Clapham and had come to help clear up.
"I think it's diabolical, what's their mentality? They have to live on these streets as well.
"If this is meant to be some kind of protest to cuts, what have they done? Just cost a load more money. It angers me."
The mother of three added: "It's parents too. All these kids who were out here last night, where are their mums and dads?
"I have three kids and I knew where all three were yesterday afternoon and evening."
