Four local authorities are launching a campaign to take control of education, social services and trading standards from their county councils.
Norwich is one of the centres calling for greater powers
Exeter, Ipswich, Norwich and Oxford want to become unitary authorities.
The towns and cities argue that they are constrained by the present two-tier system of administration.
The councils argue that unitary status would avoid the duplication that exists now through sharing power with their county councils.
Their case is backed by a report, commissioned by the councils, produced by Birmingham University's Institute of Local Government Studies.
The report says gaining unitary status would not cost extra and would in the long term would save money.
Ipswich Borough Council says it has its own identity
The report says: "The time must be right... to realise quickly all the new opportunities that unitary status should offer their communities and those in the wider regions they serve."
Laura McGillivray, chief executive of Norwich City Council, said: "We each have urban areas with pockets of deprivation which have very different needs from our surrounding county rural areas.
"We are the local authorities that can best respond to these particular community needs, yet we are constrained by the two-tier system imposed in 1974."
James Hehir, chief executive of Ipswich Borough Council, said: "Ipswich is one of the fastest growing urban centres in the UK and we think the time is right for us to have a new council.
"Ipswich has its own identity and is the cultural, economic and sporting powerhouse for Suffolk."
The councils are putting the case to the government which is looking at the reform of local government.
At present the four councils are responsible for a wide range of local services including planning, housing, waste collection, environmental health and leisure services.
While the county councils - Devon, Norfolk, Suffolk and Oxfordshire - are the main providers of education, social care, highways, trading standards and libraries.