Teachers' leaders have called for extra resources to cope with the sudden arrival of young immigrants in schools.
Warsaw to London: migrant families are straining schools, say heads
Giving evidence to a House of Lords inquiry, teachers and heads called for more language support for non-English speaking pupils in England.
Heads' leader Mick Brookes warned that the problem was most acute in rural areas and smaller towns, which lacked the support available in cities.
He also called for more accurate data about the number of migrant pupils.
The leader of the National Union of Teachers, Steve Sinnott, said that teachers had reported greater pressure on schools from an increase in pupils who did not speak English.
Speaking before the inquiry, Mr Sinnott said teachers had been "pulling their hair out" trying to accommodate unexpected arrivals.
"We have had schools in London where on a Friday afternoon the head has arrived with seven or eight youngsters and taken them to a GCSE English class, and none of the youngsters can speak English.
"Teachers want support, both in terms of knowledge and immediate support in terms of teaching materials," said Mr Sinnott.
Mr Brookes, general secretary of the National Association of Head Teachers, said that some members had complained they were at "breaking point".
He highlighted particular difficulties in Lincolnshire, Nottinghamshire and parts of south-west England.
Lack of figures
But he complained that there was insufficient information about the scale of the problem - and said it should be possible for the government to gather data from schools.
Mr Brookes said individual schools did not have the money or the capacity to absorb large numbers of newly-arrived pupils.
Schools might receive an extra £1,300 per year to support the needs of a foreign pupil, but the actual cost to the school could be £30,000, he said.
The greatest difficulty was in small schools serving an established community which faced an unexpected surge in demand for places from children of transient workers.
For example, these could be the children of eastern European agricultural workers in rural England, needing both school places and language support.
"In London, where there have been large numbers of pupils arriving from overseas, schools are already set up to support children," said Mr Brookes.
"But the real difficulty can be in more rural areas where there can be large numbers of transient workers and schools are unlikely to have that kind of language support."
There is also a question of "critical mass", he said.
While schools could absorb and accommodate the needs of a few new arrivals, it could be much more difficult when small schools were expected to admit disproportionate numbers of overseas pupils.
"It can change the nature of rural, traditional schools," said Mr Brookes.
Many of the eastern European children who entered schools learnt English very quickly and were successful students, he said - and their entry into the education system was to be supported.
But the planning for accommodating these pupils could not be left to a local level, he said.
Mr Brookes says there is a pressing need at a national level to gauge the scale of demand for places - and then to create a "thought-through" policy in response.
This will not be straightforward, he acknowledges, but needs to be addressed.
If the children are from transient communities - such as agricultural workers - then building a new, permanent school would not make sense to solve a temporary problem.
But putting immigrant children into separate, mobile classrooms would not help migrants to integrate and learn English, he said.
As well as new populations arriving in this country, there is mobility within the country, which has contributed to 758,000 surplus school places - equivalent to 2,000 empty primary schools and 250 empty secondary.
A spokesperson for the Department for Children, Schools and Families, said that extra funding was available.
Under headings including the Ethnic Minority Achievement Grant, New Arrivals Excellence Programme and the Exceptional Circumstances Grant, there is £179m funding for schools in England this year - rising to £207m for 2010-2011.