Up to a fifth of councils in England may not accept the government's offer to help pay for a freeze in council tax next year, a survey suggests.Research by the Local Government Chronicle found that 4% of respondents had already decided against a freeze.A further 16% said they were still thinking about the offer, which ministers cannot force them to accept.Local Government Minister Bob Neill accused councils shunning the freeze of "contempt for hard-working families".At last month's Conservative Party conference, Chancellor George Osborne said he was making £805m available to enable councils to extend a council tax freeze from 2011-12 to 2012-13.The government said the money would be paid for through efficiencies and involve one-off grants to local authorities to absorb planned tax rises of up to 2.5%.Money is also being offered to the Scottish and Welsh administrations, which will choose how it is spent.But, according to the chronicle's research, based on responses from 146 local authority finance directors, 116 said their councils would implement the freeze, six councils said they would refuse and 24 remained undecided.It said many councils were concerned that if council tax was frozen next year, they may have to raise it abruptly the following year.Of those who expressed an opinion on the knock-on effects of accepting the cash, 29% predicted a bigger rise in subsequent years, 18% predicted additional savings or cuts and 18% said there would be no effect.Councils in London and the South East were most likely to implement the freeze, with the North East showing most doubt, the survey suggested.Brighton and Hove Council, run by the Green party, has already decided it will increase council tax by 3.5% next year and has been criticised by the prime minister."It is a decision for individual councils," David Cameron said at prime minister's questions on Tuesday."If they want the money to go ahead with the council tax freeze, the money is there, but if they reject it, as they plan to in Brighton, that is a huge mistake, because the council will be asking families in Brighton to pay more at a time when it should be on their side."Among those expressing doubts to the Local Government Chronicle, two-thirds were Conservative-controlled councils.Last year, the scheme was adopted across England meaning average Band D bills remained at £1,439 following significant rises in previous years.But changes to the terms of the offer have left local politicians concerned about the longer-term implications of repeating the exercise.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 chronicle that the deal "financially makes no sense" and would result in a bigger-than-planned hike the following year.Local Government Minister Bob Neill said: "Under Labour, council tax more than doubled, pushing typical bills to £120 a month."This government is helping freeze council tax for two years, as well as abolishing Labour's plans for an expensive council tax revaluation which would force up bills."Town hall bureaucrats who want to hike the cost of living and shun the freeze are showing contempt for hard-working families and pensioners."Labour has said the freeze would save people about £72 a year.