Sharp council tax rises may be needed in the next few years to fund housing and education for immigrant families in Britain
The LGA, which represents local authorities in England and Wales, says rises of 6% on top of inflation-related increases may be needed in some places.
It says councils do not get enough cash to fund the services because official figures underestimate migrant levels.
But ministers say funding is fair and based on the best figures available.
The claims follow Home Secretary John Reid's call for a migration advisory committee to recommend an "optimum" level of immigration.
He is expected to flesh out his ideas in a speech on Wednesday.
LGA chairman Sandy Bruce-Lockhart says 25 councils claim inaccurate migration figures mean they do not have enough funding.
He is asking Mr Reid if he has requested more accurate immigration figures to be compiled and, if so, when they will become available.
Figures on migration to the UK are provided to the Home Office by the Office for National Statistics.
But the decision on how much money to allocate each local authority to pay for services to immigrant families, based on these figures, is taken by the Department for Communities and Local Government (DCLG).
In a letter to Mr Reid, Lord Bruce-Lockhart says: "Working migrants have become an invisible population whose children need school places, who need to be housed appropriately and in some cases need social services. Official statistics have failed to reflect this.
"Unless accurate, up-to-date figures on migration are produced so that the proper funding to councils can be reflected, this could pose severe problems in the future as services get cut, or council tax has to rise disproportionately for growing migrant population."
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