Shropshire Council is facing its first all-out elections since the unitary authority was created in 2009.
Plymouth's unitary authority city council is also believed to be involved in the waste collection talks.
Mr Lavery had been in charge at Cornwall Council since 2008, before it became a unitary authority.
Last year the unitary authority announced it had been forced to review its "non-statutory" services because of funding cuts.
The unitary authority will continue to look after a further 56 public toilets, but some charges may be introduced.
The unitary authority replaced a county council and four district councils in 2009.
Mr Turner joined the council - formerly known as Woodspring District Council, in 1989, before it became a unitary authority.
All wards were up for election on the unitary authority, which has been controlled by the Tories since it was created in 2009.
The issue of a unitary authority has also been raised - in 2007 the government rejected plans to scrap the county's six district councils.
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.
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.
That has meant that local elections are no longer held in the borough of Great Grimsby, but in the new unitary authority of North East Lincolnshire.
BBC: NEWS | VOTE 2001 | RESULTS & CONSTITUENCIES | Great Grimsby
The mayors could ask the unitary authority to consider leasing the car parks back to parish and town councils so they could work on increasing traffic.
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.
Liberal Democrat Ms Watson, vice-chairman of the Communities Overview and Scrutiny Committee of the Conservative-Independent unitary authority, said she believed planning protocol and procedures were properly followed.
The unitary authority said it was pleased services would operate until the end of October because it "ensures there will be no disruption to the holiday season".
BBC: British International Helicopter on Tresco. Pic: D.Sims
Our four shire counties (Gloucestershire, Staffordshire, Warwickshire and Worcestershire) and one unitary authority (Shropshire) all go into these elections with substantial Conservative majorities, so Labour strategists are managing expectations carefully.
They tried merely to clarify the governance of the Delta, which currently has more than 200 committees, counties, boards and departments squabbling over it, by establishing a new unitary authority.
After fighting off several challenges to his leadership, David Whalley decided to stand down as leader (and as a councillor) just ahead of the first elections to the new unitary authority.
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 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.
The council said the aim of the cemetery policy was to address the "very different" sets of fees it inherited in 2009 when it took over from the former district councils as a unitary authority.
No other single party had fielded enough candidates to claim an overall majority, although Shropshire County Council had been through many years of no overall control before the Conservatives took power in the run up to it becoming a unitary authority.
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".
Counter to Tory policy nationally, Wiltshire councillors agreed to abolish four district councils and merge into one unitary authority - saving a fortune in bureaucracy but cutting a deal with the then Labour government that none of its central funding would be reduced.
It was agreed shortly after the creation of the unitary authorities, recognising that pupils from all three local authority areas attend schools in other local authority establishments.
BBC: Clackmannanshire consultation on school holiday changes
All of these presidents, particularly Nixon and Reagan, likewise promoted a muscular vision of presidential power that strengthened the authority of government and introduced concepts, such as the unitary executive, which would become the intellectual underpinning of the Bush administration.
The police and crime panel is similar in make up to the outgoing police authority and has 20 members in Devon and Cornwall, taken from county, unitary and district councils, along with two independent appointees.
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