Crime and Policing Representatives would also be elected in Barnsley, Doncaster and Rotherham to sit on the South Yorkshire Police Authority and ensure local crime problems are resolved.

They would also decide how some police funding is spent.

But the Association of Police Authorities warned extremists such as the British National Party could hijack elections.

Chairman Bob Jones said: "Elections would reintroduce party politics to policing. There is a very real danger of extremists and single-issue pressure groups targeting these elections for their own ends."

That was dismissed by the Home Office, which said: "We believe voters will treat the opportunity seriously."

The proposals are contained in a green paper, Policing Our Communities Together, which also sets time limits for police to respond to calls.

Officers must respond to emergencies within 15 minutes, "priority cases" within one hour, telephone calls and e-mails within one day and attend non-emergency calls within two days.

It also pledges to cut bureaucracy – particularly the "stop and account" form, to be replaced by beat officers recording information by radio.

Directly-elected leaders would be created for each of South Yorkshire's Crime and Disorder Reduction Partnerships, which also include councillors, the fire service and health trusts. Elected heads of these partnerships would make up the majority on the police authority and replace councillors.

If an area agrees in the future to directly elect a mayor, that politician would also be a CPR. Doncaster's mayor would, therefore, automatically be handed beefed-up powers over policing.

But Charles Perryman, chairman of South Yorkshire Police Authority, said: "We have some reservations about the proposals, such as directly elected members of the police authority and potentially more complex lines of accountability. The Home Office seems to be assuming that if you change something it will automatically lead to improvement. The structure of local policing isn't a problem."

Home Secretary Jacqui Smith said: "The public are the best weapon to help tackle crime. That is why I'm putting them at the forefront of setting priorities."