Government proposals for elected police commissioners in radical shake-up of policing were last night branded "bizarre" and "alarming" by the chairman of the Devon and Cornwall authority they are intended to replace.

Home Secretary Theresa May yesterday announced the first election of new 'Police and Crime Commissioners' would take place in May 2012.

In the report 'Policing in the 21st Century: Reconnecting Police and the People', Ms May said the commissioners would "transfer power back to the people", better represent communities and understand "their crime and antisocial behaviour priorities".

The commissioner's role would be to "hold the Chief Constable to account" for hitting those priorities "and being able to fire her or him if they do not".

The report also laid out plans to create "Police and Crime Panels" in each force drawn from "locally elected councillors from constituent wards and independent and lay members" – immediately compared to the current police authority set-up – to hold commissioners to account.

It also said that raising the police precept – a charge which is part of council tax bills – would be subject to a referendum. None of the costs of the change, the elections, or commissioners' pay was detailed.

Mike Bull, the current chairman of the Devon and Cornwall Police Authority, said the document was "completely lacking in detail and raises as many questions as it answers" while some of its justification was "bizarre".

"The cost of the elections will be substantial," he said. "If you are having elections only for police and crime commissioners, what turnout are you going to have? It really would play into the hands of minority interests, extremist groups and single issue candidates.

"The idea of having a referendum of precept setting means the cost of that referendum will fall on the police budget. The possibility of that is quite alarming."

The current annual running costs of the police authority is around £1.2 million, which Mr Bull said was just 0.56 per cent of the overall force budget.

Mr Bull said there was no indication of the cost of the new system but said the change was wrong in principle.

"I don't believe it is realistic for one person, however capable, to represent all our communities, to have contact with them or even be known across Devon and Cornwall," he added. "It just won't happen."

The move to police commissioners is among a raft of proposals which Ms May described as "the most radical reforms to policing in at least 50 years".

Plans were also announced to establish a new National Crime Agency to lead the fight against organised crime, cut police bureaucracy, free up officers' time and give the public more involvement.

Prime Minister David Cameron said: "It is vital police officers are free to tackle the crime and antisocial behaviour that matters most to people, not tied-down by bureaucracy and form-filling.

"The fundamental reforms we are announcing continue our work to deliver a police service that is visible and accountable to the very people it serves in communities up and down the country.

"By replacing invisible police authorities with directly elected Police and Crime Commissioners, we can forge a direct link between the police and the public."