Rank and file police officers are "angry" at the Prime Minister's decision to contact US "supercop" Bill Bratton, a Police Federation official has said.
Ex-New York police chief Bill Bratton believes crime-fighting solutions that worked in America can also work in the UK.
Ian Hanson, chairman of Greater Manchester Police Federation, urged Mr Cameron to listen to those who "live and police the communities affected" rather than "someone who lives 5,000 miles away".
Mr Bratton, a former New York police commissioner who is to advise the Government in the wake of rioting across England, believes crime-fighting solutions that have worked in America can also work in the UK.
But Mr Hanson, whose force tackled hundreds of rioters in Manchester city centre and Salford on Tuesday night, told ITV news it is "absolutely incredible" that the Prime Minister had asked for the American's advice.
"What we've witnessed this week has been British policing at its absolute best," Mr Hanson said.
"There is anger, there is disappointment, a degree of incredulity as well. We're local people who live in the communities, who work in the communities and police them. He needs to speak to us, not someone who lives 5,000 miles away."
Mr Hanson said there were not enough police officers at the start of this week's riots because the Government has cut police numbers.
He added: "One thing that Bill Bratton did when he took over in New York in 1994, was he increased the establishment of New York City police by 5,000 officers. How an earth are we going to replicate that with cuts approaching 30,000 police officers?"
Reacting to the riots, Mr Bratton said British police needed to focus on calming racial tensions by working more with community leaders and civil rights groups. He also said employing more minority police officers could be a potential long-term solution to stopping any future disorder.
The 63-year-old, who is now a security consultant, will meet Mr Cameron next month.