Senior police officers were in open revolt over the government's police reform agenda on Friday, reacting furiously to criticism of the way they handled the riots, and turning their fire on the home secretary, Theresa May, after she suggested she had instructed the police to take a tougher line.

Faced with an onslaught from all levels of the police, David Cameron tried to beat a retreat, lavishly praising the force after he and May had described police tactics in the Commons on Thursday as timid and highlighted police admissions that their initial plans to counter looting had been misguided.

Cameron is understood to have phoned Tim Godwin, the acting Metropolitan police commissioner, on Friday and the message was posted on the Met's internal communications system for its staff.

It read: "The prime minister has this morning telephoned the temporary commissioner, Tim Godwin. He wished to express his personal thanks and admiration to the entire command team, gold, silver, and bronzes – and all the many officers and staff who have worked so hard during the recent disorder."

May said on Wednesday she had insisted that special constables be mobilised and all police leave should be cancelled, remarks that were seen to threaten the cornerstone of police operational independence.

Sir Hugh Orde, president of the Association of Chief Police Officers, described the role of the politicians as "an irrelevance", pointing out that by Monday the police had decided to mobilise huge numbers of officers in London.

He said he briefed Cameron about the decision after the prime minister returned from holiday on Tuesday morning. Derek Barnett, president of the Police Chief Superintendents' Association, also said the return of the politicians did not make any difference.

"The decisions to deploy police officers in large numbers was made well in advance of politicians becoming involved," he said, adding that the point of politicians returning from holiday was only to give "a sense that there is now someone back in charge of the country and offering political leadership".

Asked about claims by Cameron that policing had been too timid, Godwin said: "I think, after any event like this, people will always make comments who weren't there."

He insisted that the changes in tactics and police numbers were due to commanders, not politicians. "I think the issue around the numbers, the issue around the tactics – they are all police decisions and they are all made by my police commanders and myself."

Political sources described Orde as incandescent with Tory attempts to take credit for toughening the police line, adding that it underlined his fear that government plans for elected commissioners will politicise the police.

The sources added that Orde was still interested in becoming the new Metropolitan police commissioner, but only on his own terms.

The row came as an ICM poll for the Guardian showed that the public sided with the police and not the politicians over the handling of the riots. The poll conducted this week shows that less than a third of voters think the prime minister or the London mayor, Boris Johnson, have performed well.

Only 30% say Cameron has done a good job, against 44% who say the opposite. For Johnson, the figures are 28% good job and 38% bad. But, 45% think Godwin has done well, against 27% who say he has not. The ICM poll also showed most are concerned that the police, facing 20% cuts in budgets, already do not have enough resources.

After a meeting of the government's Cobra committee, Orde told MPs: "Let us be clear about one thing – the distinction between policing and politics remains. The police service will make the tactical decisions and quite rightly we must and should be held to account."

Earlier this week he had ridiculed a suggestion by Cameron that water cannon should be put on standby, saying they would be entirely useless.

Orde revealed he had urged May to hold a conference on comparative international policing styles, adding pointedly: "I sense if we do that, the British model will come out well on top."

Bill Bratton, the former US policeman admired by Cameron and credited with cleaning up New York, said he has agreed to help the UK government on how to deal with gangs. Bratton, who is now chairman of private security firm Kroll, spoke to Cameron by telephone on Friday to discuss the matter.

"I'm being hired by the British government to consult with them on the issue of gangs, gang violence and gang intervention from the American experience and to offer some advice and counsel on their experience," Bratton told Reuters last night. Downing Street said Cameron thanked Bratton for agreeing to a series of meetings in the UK this autumn to share his experiences tackling gang violence. Bratton will provide counsel "in a personal capacity," it said in a statement.

"This is a prime minister who has a clear idea of what he wants to do," Bratton told Associated Press. "He sees this crisis as a way to bring change. The police force there can be a catalyst for that. I'm very optimistic."

Mr Bratton and Cameron are expected to meet next month to continue their talks.

Orde set himself against Cameron's plans to allow outsiders to join the force at high ranks, saying: "The leadership of this service understands policing. We all started where our brave officers were the other day. We start at the bottom, we move up and we learn and we move on."

He also contradicted Cameron's claims that 20% cuts to police budgets in the next four years would have no impact on police visibility. He said: "Chief constables have minimised the impact on the frontline. We will have to have some very honest, straightforward conversations with government in years three and four. We have to understand what sort of service we want and what we want it to do, and not do."

Peter Hain, the former Northern Ireland secretary who worked with Orde in Northern Ireland, offered his strong support, saying: "He is a reformer that stands up for his officers and tells it like it is in a non-party political way. The Conservatives would be mad not to appoint him Metropolitan commissioner if he wants the job, but he will do it only on his terms."

Sir Norman Bettison, chief constable of West Yorkshire, opened another front against government plans to introduce elected police commissioners to oversee chief constables, with elections due next May at a cost of £100m. He said the mutual aid programme which saw 16,000 officers put on to the streets of London would not work with elected commissioners.

"Mutual aid relies upon the unfettered ability and operational discretion to do things for the greater good rather than for local popularity. The surge the prime minister talks about can only be achieved by coordinating assets across 43 forces. If there are elected police and crime commissioners this will not happen. Each will have been elected on different political platforms and there will be all sorts of parochial decision making about their priorities."

Despite the scale of the riots, and claims that the police mishandled the initial disorder in Tottenham, public trust in the police seems uniformly strong. Overall, 61% of those polled say they are confident that the police enforce the law fairly, uniformly and without prejudice, while 36% say they are either not at all (10%) or not very (26%) confident.

There is some evidence that younger or poorer people are less likely to trust the police than older or better-off ones, but in all categories, a majority are satisfied.

However, the public are less confident about the police's ability to keep order. A majority say they think the police lack sufficient resources. The finding could add to opposition to cuts in police numbers and funding. In the Commons on Thursday, Cameron came under fire from the Labour leader Ed Miliband and some backbenchers over plans for cuts.While 41% say they are either very (6%) or quite (35%) confident the police have been given adequate resources, 56% say the opposite.

People on lower incomes are the most likely to think the police are under-resourced.