Council leaders laid down a challenge to Local Government Minister Ruth Kelly as they gathered in Bournemouth for their annual conference today.
Ms Kelly will speak today at the Local Government Association gathering, attended by Birmingham City Council deputy leader Paul Tilsley.
Ministers have promised to devolve control over transport, planning and economic development to councils - as long as they accept the need for strong and visible leadership, such as a mayor.
But the LGA has drawn up a list of its own demands, which include giving far more power to individual councillors.
It set out key proposals, including slashing #2.5 billion of Whitehall red tape and giving councils extra powers over transport, planning, economic development and skills - even if they keep their existing leadership structure.
The LGA called for local authorities to set their own business rates, a suggestion that is fiercely opposed by business leaders.
It also said local councillors should have the right to summon NHS chief executives and police chiefs to answer questions at public meetings, and to speak out on issues which affect their wards without being accused of having a vested interest.
The Government should also accept that giving councils more freedom will mean that some provide better services than others, the LGA said.
It said this was "postcode choice", rather than a postcode lottery.
The Government wants to create city regions, where councils such as Birmingham would join forces with neighbouring authorities to create a body with its own leadership and strong decision-making powers.
Although the LGA does not oppose this idea, it is encouraging Ministers to give more power directly to councils.
LGA chairman Sandy Bruce-Lockhart: "We have a consensus across Westminster that we need a decentralising, devolving and deregulating agenda in order to improve public services and strengthen local democracy."
He warned: "We see an erosion of democracy, a crisis of trust, a cynicism with politicians and with the ability of seemingly unreachable governance to deliver solutions.
"We must give people back power and influence over their lives, their local services, and the future of the places where they live."
He added: "The time has come for audacious and deepseated reform. We look forward to the Minister providing a timetable and blueprint for devolving, decentralising and deregulating local government at the LGA conference this week.
"Local government is coming up with the route map and readying itself for the immense task ahead.
"We call upon central government and the new minister to join us on this journey to a better future for all."
Conservative Party leader David Cameron will speak at the LGA conference tomorrow.
The Tories have also promised to give much more power to local councils.
They back a city region if it means local councils making decisions together, but accuse the Government of planning to create a new and unnecessary regional tier of government.