Norwich, Exeter and Ipswich are among 16 councils applying for unitary status to have been shortlisted for further consideration, the government says.
Two-tier authorities "caused confusion" about responsibilities
Minister Phil Woolas said cutting one of the two tiers of councils - district or county - could save £200m a year.
He also shortlisted bids from Cornwall, Cumbria, Durham, North Yorkshire, Shropshire, Somerset and Wiltshire to become the sole council in their areas.
If approved the district councils in those counties would disappear.
Bedfordshire County Council
Bedford Borough Council
Cornwall County Council
Cheshire County Council
Chester City Council
Cumbria County Council
Durham County Council
Exeter City Council
Ipswich Borough Council
North Yorkshire County Council
Northumberland County Council
Norwich City Council
Shropshire County Council
Somerset County Council
Wiltshire County Council
There will now be a 12 week consultation with the final decision being taken in July, with the new structure coming into place in April 2009.
Local authorities had to fulfil criteria relating to affordability, strong leadership, improved public services and support. Twenty six councils had applied for unitary status.
Local government minister Mr Woolas said an example of confusion was where grass verges were maintained by the parish council, the pavement was kept clean by the district council, while the county council looked after the road.
The restructuring was included in the Local Government White Paper last October.
Mr Woolas said: "The bids that local authorities submitted show that they are up for improving the services they offer to their communities by making them more responsive, effective and efficient.
"We have been impressed by their quality, value for money and their cross section of support which is why we can now go much further and proceed to the next stage in 13 areas."
While North Yorkshire County Council had gone through to the next stage, district councils in the area were not pleased.
"Creating one council would produce an authority too remote to deliver truly local services or community leadership," said Peter Simpson, from Hambleton District Council but speaking on behalf of all the district councils in North Yorkshire.
"There is no need for a complicated restructuring that is someone else's solution to an ill-defined problem."
The region's 580,000 residents would be surveyed about their views of a single council covering its 3,103 sq miles.
"District council leaders are concerned that nowhere in all this consultation does the public feature - the very people that this reorganisation affects and who will end up paying for it in some way," he said.
The ten unsuccessful bids came from Cornwall districts; Durham district; East Riding UA East Riding and Selby; Ellesmere Port and Neston Borough Council; Lancaster City Council; Mid Bedfordshire District Council and South Bedfordshire District; Oxford City Council; Pendle Borough Council and Burnley Borough Council; Preston City Council; and South Somerset District Council.