Conservative candidate Antony Little said the plan for a unitary council was "not affordable" and "has no measure of support by local people".
But he said he had concerns about the "shambolic process" and was concerned as to whether the boundary for the new unitary council was large enough.
Cornwall produces about 300, 000 tonnes of waste a year and, according to the Conservative-Independent led unitary council, the county will run out of landfill space by 2014.
Plymouth's unitary authority city council is also believed to be involved in the waste collection talks.
The neighbouring unitary Plymouth City Council has certainly had its up and downs since it was created in 1998.
The last local election was held in Wiltshire four years ago, when the county council and North Wiltshire, Kennet, Salisbury and West Wiltshire district councils came together to form a unitary authority - Wiltshire Council.
Unison's figures are based information from the Office for National Statistics on the number of Job Seekers' Allowance claimants per unfilled job centre vacancy in each of the region's council and unitary authority areas.
The unitary authority replaced a county council and four district councils in 2009.
Councillor Lance Kennedy, cabinet member for community safety of the Conservative-Independent led unitary authority, said the council was to lobby the environment ministry Defra for reassurances.
The council said it breached the Newport Unitary Development Plan.
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Although the policy has already been adopted by the national park, it will still be open for scrutiny as it is included in the draft Joint Unitary Development Plan drawn up with Pembrokeshire County Council.
But Devon County Council leader Brian Greenslade said the council was relieved by the government decision, as Exeter City Council's proposal for a unitary authority was "deeply flawed and could not have worked within the narrow confines of the city boundaries".
Mr Lavery had been in charge at Cornwall Council since 2008, before it became a unitary authority.
Mr Turner joined the council - formerly known as Woodspring District Council, in 1989, before it became a unitary authority.
The Council of the Isles of Scilly is also a unitary authority which looks after roads, waste disposal, planning, education, licensing, St Mary's Airport and much more.
Shropshire Council is facing its first all-out elections since the unitary authority was created in 2009.
It has the lowest council tax in Kent and one of the lowest charges among unitary councils across England.
The inaccuracies came to light following an independent investigation commissioned by the council, which took over responsibility for the cemeteries after it became a unitary authority.
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