Government statistics underestimate the true number of immigrants, leading to under-funding and a burden on services, says the Local Government Association.
Slough has seen a surge in migrant numbers, says its council
The inclusion of eight eastern European nations into the European Union has led to a surge in immigrants, it says.
LGA chairman Sir Sandy Bruce-Lockhart said government figures were no longer adequate for calculating an area's financial needs.
As a result, the government was refusing to fund services, he said.
"It is totally unacceptable that the government has no proper information on [migrant] numbers," he told BBC Radio 4's Today programme.
"[The government] has not got information and therefore it is refusing to fund the services, although it has been advised by the Office of National Statistics that that would be a sensible thing."
Cheryl Coppell, chief executive of Slough Borough Council said migration statistics for the area were "woefully inadequate".
Over the past 18 months, some 9,000 new National Insurance numbers have been issued in Slough - which is west of London - of which 150 went to British nationals.
In contrast, the Office for National Statistics recorded 300 international migrants settling in the town in 2004.
However, government statistics - on which the allocation of central funding is calculated - show the borough's population falling.
This, says the council, will cost it £15 million between now and the next census in 2011.
Ms Coppell said: "Because the government's figures are now woefully inadequate to represent Slough's population, we just simply don't have the money we need to provide basic services.
"We are having to consider cutting a lot of the things we would like to do for local people."
Ms Coppell also said the influx of newcomers from Poland and other eastern European countries was threatening the social cohesion of the town, which already has 37% ethnic minority residents.
"Slough has a very good reputation for social cohesion, but we are now being pushed to stretching point and we are very worried that some of these new incoming communities are having displacement effects on our existing communities," she said.
"For example, we have seen Pakistani employment rates fall over the last few months, and we believe that that is because some of the new incoming migrants are taking their jobs."
The council says it has had an increase in the number of overcrowded houses, with 50 complaints being made in the past six months.
It says a migrant influx into the area had led to such problems, with as many as 15 migrant workers in a single house.