Up to a fifth of local councils may put up council tax next year despite David Cameron warning it would be a "huge mistake" to opt out of a Government offer to freeze it.
A survey of town hall finance chiefs by the Local Government Chronicle (LGC) found a fifth were undecided whether to adopt the scheme - while 4% had already decided not to.
Among those expressing doubts, two-thirds were at Tory-controlled councils.
It was confirmed last week that the Government would again offer one-off grants equivalent to a 2.5% hike in the levy to councils which did not raise bills.
Last year, the scheme was adopted across the board meaning average Band D bills remained at £1,439 following significant rises in previous years.
Changes to the terms of the offer have left local politicians nervous about the longer-term implications of repeating the exercise however.
Unlike the previous tranche, there will be no funds provided to protect councils against knock-on effects of the freeze in future years, local government bosses have warned.
One finance director of a Tory-controlled district told the magazine that the deal "financially makes no sense" and would result in a bigger-than-planned hike the following year.
"But politically members feel they've no choice," he added.
Others said deeper service cuts would result. Based on responses from 146 finance directors, 116 said their councils would implement the freeze, six councils said they would refuse and 24 remained undecided.
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