Anyone who swears at a police officer must expect to be arrested as part of a zero-tolerance approach in the wake of the London riots over the summer, the London mayor, Boris Johnson, has said.

In a speech to the Tory party conference that highlighted falling crime rates in the capital, Johnson warned the Conservative-led government that he would not tolerate police numbers falling below safe or reasonable levels on his watch.

The mayor – one of the party's most popular figures – was given a standing ovation at either end of his keynote speech as he highlighted his record in office and laid out his plans to avoid further riots.

In a swipe at the justice department, Johnson spoke out against guidance instructing police not to arrest people hurling abuse at them.

To applause, he told Tory delegates that officers needed backing in dealing with insults in order to set boundaries and ensure people to not go on to commit more serious offenses.

Johnson – who has delegated the chairmanship of the Metropolitan Police Authority to his deputy mayor Kit Malthouse – said that while three-quarters of those arrested in the summer riots had previous convictions, the rest had none.

He lauded the work of his new Met police chief, Bernard Hogan-Howe, who was previously chief constable of the Merseyside force and oversaw a 40% reduction in crime during his tenure.

Johnson said Hogan-Howe, appointed last month, understood what the mayor called the Capone principle – that "if you crack down on the small stuff, the big stuff takes care of itself".

"If people swear at the police, they must expect to be arrested," he said. "Not just because it's wrong to expect officers to endure profanities, but it's also because of the experience of the culprits.

"If people feel there are no comebacks, no boundaries and no retribution for the small stuff, then I'm afraid they will go on to commit worse crimes."

He suggested a new law would need to be established to clear up the confusion over police powers to deal with people swearing at them.

Although no specific offence of swearing at a police officer exists, it is an offence under section five of the Public Order Act 1986 to "use threatening, abusive or insulting words or behaviour within the hearing or sight of a person likely to be caused harassment, alarm or distress thereby".

Johnson's initial response to the riots was widely criticised at the time, with many angered by his delay in returning from a family holiday in Canada.

A YouGov poll conducted in mid-August found 54% of respondents saying the mayor had handled the riots badly. However, his subsequent call for the government to rethink police budget cuts was welcomed by the opposition.

He told an audience including David Cameron that he had spent a "fair bit" of the past two months speaking to people affected by the riots and had been left with a "pretty good idea of what Londoners want".

He said: "They want to make sure nothing like it ever happens again. As long as I am mayor, I will not allow police numbers to fall below a level that I believe is safe or reasonable for a great city like London.

"Police numbers are up by 1,000 since I was elected, and the number of special constables has doubled to more than 5,200 – and I pledge to you I am going to keep it that way."

Critics have pointed out that the mayor is responsible for police numbers in the capital and that, this year alone, London has seen a 4% drop in police numbers.

Johnson said Londoners wanted politicians, teachers, and parents to sort out the underlying issues that caused the riots.

On Monday, he announced that he will fund boot camp-style clubs next summer, aimed at instilling discipline and motivating disengaged youth.

The "tough love" after-school clubs will begin at around 25 schools in the capital.

He also used his speech to highlight his Team London project – an umbrella organisation set up for anyone interested in volunteering in the capital – and said his vision was to "put the village back into the city".

Johnson is seeking re-election in a May rematch with Ken Livingstone, midway through the coalition's current term.

Many Conservatives are privately surprised at how well Tory support is holding up as spending cuts begin to bite, and hope the mood continues as the party heads into the mayoral race. A stall devoted to Johnson was placed just outside the conference hall, with delegates invited to volunteer for his re-election campaign.

Cameron said he was right behind his fellow Old Etonian, telling told LBC Radio on Tuesday: "At a time of economic difficulty, I think he brings strong, charismatic leadership, he brings people together, he cheers people up.

"I am right behind him, because I think the last thing London needs is a return to Red Ken."

Livingstone last week announced plans to cut transport fares in the capital by 5% if he is re-elected, but city hall claims the move would pull crucial investment from London's public transport system.

Lauding the government's decision to invest in London's infrastructure, Johnson said: "Thanks to the common sense of this coalition government, the settlement we got last year, we not only have the Tube upgrades, we have Crossrail and Thameslink.

"I will not allow that investment and these vital improvements to be jeopardised for a short-term political gain."

In a direct address to Cameron, he added: "I say to my friends in the Treasury – not all of whom I see here; well, Dave's here – Franklin D Roosevelt offered a new deal. I give you the wheel deal: you help us to invest in transport infrastructure, and we in London will supply the locomotive of the UK economy."

Livingstone said Johnson's speech showed the mayor was out of touch.

"Today we saw the real Boris Johnson – an out of touch Conservative, failing to put ordinary Londoners first on the issues that really affect them, from rising fares to police cuts.

"He gave no hope to Londoners facing another steep fare rise this January, which will mean bus fares are up 56% under a Tory mayor, and gave no hard commitment on police numbers, which are in fact due to fall by 1,800 according to his own Metropolitan police figures."