Councils want to go ahead with planned elections
Emma Howgego/BBCLocal authorities in Cambridge and South Cambridgeshire say they will not ask to postpone elections this year.
Councils have been told they can apply to postpone the polls in order to focus on local government reorganisation.
They have until Thursday to let the government know if they want to do this.
However, the leaders of Labour-run Cambridge City Council and Liberal Democrat-run South Cambridgeshire District Council say they do not want postponements.
Cambridge City leader Cameron Holloway said the council had "the capacity to go ahead with elections this year while also making a success of local government reorganisation".
Bridget Smith, who leads the South Cambridgeshire authority, criticised the government's offer, and said: "It is not right for central government to be demanding that councillors decide whether residents should be denied the opportunity to vote or not. "
Huntingdonshire District Council and Peterborough City Council are due to hold meetings next week, when councillors will vote on whether to request postponements.
Elections are scheduled to take place on 7 May. Elected members normally serve four-year terms.
But with a new local council structure due to come into effect in 2028, those elected this year will serve two-year terms.
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