The former national head of counter terrorism is to lead an inquiry into 25 Birmingham schools over allegations of a hard-line Islamist takeover plot.
But the appointment of Peter Clarke, an ex-deputy assistant commissioner of the Met, was described as "desperately unfortunate" by the chief constable of West Midlands Police, Chris Sims.
The Department for Education (DfE) has appointed Mr Clarke to review evidence.
Birmingham City Council said it had more than 200 reports over its inquiry.
Mr Sims added: "Peter Clarke has many qualities but people will inevitably draw unwarranted conclusions from his former role as National Co-ordinator for Counter Terrorism."
Mr Clarke's background includes leading the investigation into the London 7 July bombings, in 2005.
The city council's Labour leader, Sir Albert Bore, said: "He [Mr Clarke] will have to build relationship with the community, the community of Birmingham, the Muslim community of Birmingham.
"And coming with a background which is that of counter-terrorism doesn't make for a good starting point.
"I think many of the community in Birmingham would not want an investigation to be conducted along those lines because they do not believe that the activities in the schools are the starting point for terrorism in the city."
Khalid Mahmood, Labour MP for Birmingham Perry Barr, also questioned the appointment.
"It's the perception that it gives to people across the country - that this is an issue of terrorism, not about structures and how schools work," he said. "And that would be detrimental to the Muslim community, not just in Birmingham, but across the whole country."
The so-called "Operation Trojan Horse" letter, which came to light in March, purported to outline a template on how schools could be pushed into adopting more Islamic cultures.
Apparently written by someone in Birmingham to a contact in Bradford last year, the undated and unsigned document proposed a co-ordinated effort of installing governors and replacing staff - including head teachers - who were unsympathetic to Muslim doctrines.
It claimed the tactics had been successfully deployed at several schools in Birmingham.
Mr Clarke, who has been appointed education commissioner, is due to report back with his findings in the summer and his remit will cover local council-run primary and secondary schools as well as academies.
Explaining the appointment, Education Secretary Michael Gove said: "I have already asked Ofsted to inspect a number of schools of concern and these investigations are ongoing.
"But wider, more comprehensive action is needed.
"These allegations need either to be substantiated and firm action taken, or to be shown to be baseless.
"We cannot allow uncertainty for parents or pupils to persist."
A DfE spokeswoman said Peter Clarke's background made him "exactly the right appointment for this important job" and that he had worked for many years with diverse communities.
"He has long experience of leading sensitive investigations, and has earned a reputation for thoroughness, integrity and independence," she added.
But Bob Jones, the elected West Midlands Police and Crime Commissioner, said: "My main concern is that the Secretary of State is attempting to divert attention away from the governance and diversity issues that might be embarrassing to his policies and approach to school governance."
The DfE said Mr Clarke would be responsible for analysing "evidence of extremist infiltration in both academies and council-run schools".
The department said Mr Clarke would be accountable to Mr Gove and would work closely with the city council, which has appointed former head teacher Ian Kershaw as its own chief advisor for the inquiry.
Norman Smith, the BBC's chief political correspondent, said government sources had denied Mr Clarke's appointment was evidence of a possible terrorist link.
He added sources said Mr Clarke had been appointed because he was a "top policeman who will get to the bottom of what has been going on".
The council's investigation, running in parallel to the DfE's inquiry, is due to initially report back in May.
Ofsted has been sent in to inspect 15 Birmingham schools in recent weeks, after the Trojan Horse allegations first broke.
The Society Of Local Authority Chief Executives said the involvement of so many bodies in multiple investigations "demonstrated the confusion caused by recent reforms and highlighted the need for clearer lines of responsibility".
With the spread of academies, free schools and others outside of the local authority's control, the society said the accountability system for schools in England was "broken and in need of urgent review".
Since the Trojan Horse letter surfaced, a number of school staff have come forward to make various allegations.
These include claims of boys and girls being segregated in classrooms and assemblies, sex education being banned and non-Muslim staff bullied.
Park View Education Trust, which was implicated in the original document, has rejected claims of a takeover.
Its chairman Tahir Alam said it was facing a "witch hunt" based on "all sorts of false allegations" and an internal investigation had found no evidence to substantiate the claims.