Police chiefs have defended their handling of this week's riots despite criticism from the prime minister.
Association of Chief Police Officers president Sir Hugh Orde rejected suggestions that the restoration of calm was due to political intervention.
Acting Met Police commissioner Tim Godwin said comments were being made by people "who weren't there".
David Cameron said police did make mistakes over numbers and tactics - but also praised the bravery of officers.
Mr Godwin denied police had been too "timid" in their initial response to the riots on Saturday - but he said that "if police officers had the benefit of hindsight as foresight we would obviously do things slightly differently".
Ministers and police chiefs have clashed over who was responsible for bringing about a surge in police numbers on the streets of London from 6,000 on Monday to 16,000 on Tuesday.
Mr Cameron returned from holiday on Monday night and called an urgent meeting of emergencies committee Cobra.
Communities Secretary Eric Pickles said the prime minister had been "very much in charge" of that meeting.
But Sir Hugh - who is seen as a leading contender to become the next Met Police commissioner - told the BBC that the subsequent restoration of calm on Tuesday night had not been down to political intervention.
"The fact that politicians chose to come back [from holiday] is an irrelevance in terms of the tactics that were by then developing," he told BBC Two's Newsnight.
"The more robust policing tactics you saw were not a function of political interference; they were a function of the numbers being available to allow the chief constables to change their tactics."
Senior police sources have told the BBC that plans to increase officer numbers in London were well advanced before the Cobra meeting on Tuesday.
BBC home affairs correspondent Danny Shaw has learned that Scotland Yard made several calls to the Police National Information Co-ordination Centre on Monday requesting additional support.
Home Secretary Theresa May said she spoke by conference call to all police chiefs on Wednesday and "ordered that all special constables should be mobilised, all police leave should be cancelled and the robust tactics used on Tuesday by the Metropolitan Police adopted by all forces dealing with public disorder".
But Sir Hugh said she had "no power whatsoever" do that - and decisions about staffing were a matter for force commanders.
He later denied there was any rift with the government and said the home secretary had given him "quite outstanding" support.
"She has praised police officers. She understands the complexity of the world in which we live and I think she very clearly understands that we cannot get it right all the time," he said.
"But let's be very clear on one thing - the vital distinction between policing and politics remains. The police service will make the tactical decisions, and quite rightly and robustly, we should and must be held to account [by politicians]."
Mrs May also sought to play down any suggestion that the government's was seeking to take credit for restoring calm, insisting: "What I accept is that the people who got the riots under control were the police."
The prime minister said police chiefs took the decision to increase officer numbers and change tactics, and the Cobra meeting helped commanders "by showing there was political backing for the changes they wanted to make".
But Police Federation vice-chairman Simon Reed said the suggestion that police had changed their approach after the government stepped in was "a cheap shot" - and Sir Hugh was "clearly upset".
"It's a slight on the professionalism of the police service and the rank and file because some of the language, some of the tone used, was that they were too timid - almost that they weren't brave enough.
"Rank and file officers will be very upset about those comments because these were unprecedented levels of violence that we saw."
Ian Hanson, chairman of the Greater Manchester Police Federation, also said it was "disingenuous of politicians to say that they [had] sorted the problems out".
Labour have said the riots show that planned cuts to police budgets - and in turn, officer numbers - should be abandoned.
Shadow Home Office minister Vernon Coaker told the BBC the government should be given the same sort of protection from spending cuts as the health and education sectors.
And he accused David Cameron and Theresa May of "playing politics" with policing and trying to "take the credit for tough and correct action taken by the police while at the same time trying to pass the buck for any criticisms back to them".
The Police Federation said that if the riots had happened in a year's time - with "10 or 12,000 fewer officers" - police would not have been able to mobilise resources in the way they have done this week.
But during Thursday's debate, the prime minister insisted the cuts were "totally achievable" without any reduction in the visible policing presence and said that a "surge" of officers - as seen in recent days - would still be possible in future.
In other developments:
- Richard Mannington Bowes, a 68-year-old man who was critically injured in an attack as he tried to stamp out a fire during riots in Ealing, has died. Police have launched a murder inquiry and a 22-year-old man has been arrested
- Magistrates again sat throughout the night on Thursday in London to hear the cases of some those arrested during the violence. Courts also sat late into the evening in Birmingham and Manchester
- The prime minister announced a crackdown on facemasks and a review on the use of curfews
- A man has been arrested over an attack on a Malaysian student who was assaulted by rioters in east London and mugged by people who had initially appeared to be helping him
- More than 100,000 people have signed an online petition calling for anyone convicted of taking part in the riots to lose any benefits they receive