Elections are due to take place in 21 county council areas in England in May, as well as some unitary authorities and elections for some regional mayors.
When it announced its devolution plans in December, the government suggested some of these elections, especially in county councils, could be delayed by a year or more. Scheduled mayoral elections will not be affected.
Under the plans, announced by Deputy Prime Minister Angela Rayner, smaller district councils and larger county councils could be merged to create single councils to handle all services.
Ministers see the reorganisation of local government as a key part of their plan to devolve powers out of Westminster to local communities.
Local government minister Jim McMahon wrote to councils in affected areas asking them to express their interest in taking part.
Several councils are holding urgent meetings this week to decide whether to press ahead.
County councils that have indicated they are interested and could see elections postponed include:
Devon
East Sussex
Essex
Gloucestershire
Hampshire
Kent
Norfolk
Suffolk
Surrey
Warwickshire
West Sussex
Worcestershire
Ministers will make the final decisions on whether local elections are postponed.
Conservative shadow housing secretary Kevin Hollinrake said restructuring local councils should not deny voters a voice, nor delay local democracy by more than a year.
“No council should be bullied or blackmailed into local government restructuring,” he said.
“It should not be imposed through top-down Whitehall diktat by the Labour government.
“By definition, devolution should be about local decision-making.”
Cllr Kevin Bentley, the Conservative leader of Essex County Council, said it was a “once in a lifetime chance to improve outcomes for Essex”.
Cllr Tim Oliver, the Conservative leader of Surrey County Council, said: “We owe it to Surrey’s residents to get the best devolution deal possible for our county.”
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