Many larger schools, including secondaries, have coped well with the influx, drawing on the experience of coping with previous waves of immigration.
But some primaries, especially in rural areas, are struggling to cope with even a handful of pupils who cannot speak English.
One teacher, who asked not to be named, said: "Many teachers are spending much of their own time, effort and money in trying to make resources in order to teach these children because the local authorities are not coming up with the much needed help and support.
"Why should teachers spend their own money doing this?"
Ninety-four per cent of the local authorities that responded to a National Union of Teachers questionnaire said they had seen a rise in the number of pupils needing ethnic minority and English language support in the past 18 months.
But the survey, published this week, also found that changes to funding for these students may mean that some are missing out on the help they need, possibly because schools are spending it on other areas of the curriculum.
Around a third of the 36 local authorities that responded to the survey said they were not confident that Ethnic Minority Achievement Grant (Emag) funding was being used by schools for its intended purpose.
And despite the apparent demand for their services, a quarter of the 58 Emag-funded teachers surveyed said they had been given less employment and lost management allowances.
Steve Sinnott, the NUT's general secretary, said some headteachers were spending the funding on other aspects of the curriculum.
"It should be a full local authority service, not something organised by a private service or on an ad-hoc basis within the school," he said.
"Teachers with responsibilities in this area should be given the status and extra payments they deserve."
Last year, six Polish children arrived at the 340-pupil Bengeworth first school in Evesham, Worcestershire. Headteacher David Banham has taken money from his school budget to bring in a teaching assistant because extra funding will not arrive until next year.
"It is an issue for us financially, and it's more work for the class teachers themselves," he says. "But they add a different flavour to the school and the rewards are great."