Members of the highly respected National Association of Headteachers will this week tell Parliament that the issue is starting to change the culture of some schools. Some heads said the issue was 'out of control'.

While praising the ability of the new pupils, many of them from eastern Europe, and emphasising that they should be welcomed into schools, headteachers are concerned they do not have the amount of money needed to cope with the issue.

'There is a feeling among some of our members that this is out of control and unpredictable,' said Mick Brookes, general secretary of the NAHT. Brookes, who will give evidence this week to a Parliamentary inquiry investigating the impact of immigration on British society, added: 'Some schools just don't know how many migrant children they will have to admit.'

He said that while schools could absorb one or two foreign pupils, some were struggling with the sudden large increase in the numbers of children from overseas: 'If you get a sudden influx not only will it strain or even break the resources of the school, it will also change the culture of that school.'

Clarissa Williams, head of Tolworth Girls' School in Kingston upon Thames, south London, said she received £1,300 a year from the government to cover the costs of teaching English to foreign pupils but was having to spend £30,000 of her own budget to keep pace.

'These children just appear from nowhere,' Williams said. 'They turn up on your doorstep and if you have space you have to make the necessary arrangements. It places a significant additional strain on budgets.'

On Tuesday the association will tell the House of Lords economic affairs committee that education budgets have not kept pace with the increase in the number of pupils for whom English is a second language, or not spoken at all, who have entered Britain since the European Union expanded three years ago.

The ethnic minority achievement grant, the main funding stream for schools, has increased marginally from around £160m to just under £180m since 2005, when countries from the former eastern bloc joined the EU. But over the past three years, hundreds of thousands more migrant children have entered Britain's education system.

Figures compiled by the Institute for Public Policy Research think-tank show that, since EU expansion, there are now some 12,900 children from the Czech Republic in British schools, 30,400 from Lithuania, 170,000 from Poland and 28,700 from Slovakia. 'It's important all children are welcomed into schools and that they feel partt of the community,' Brookes said. 'But there is a lot of pressure on school capacity to absorb these additional children.'

Experts suggest the pressures are being felt particularly in some rural schools that until now have experienced little of the impact of migration. With foreign workers now filling agricultural vacancies in such counties as Lincolnshire, some schools now find themselves accommodating significant numbers of foreign pupils. Last year 96 children who did not speak English unexpectedly joined primary schools in Boston, Lincolnshire, alone, more than doubling the number attending the previous year.

'This can have a real impact on school league tables,' Brookes said. 'We need to look at how we deal with the new challenges facing these sorts of schools.'

Jill Rutter, a senior research fellow with the IPPR, said it was time for the government to reassess the provision of English language teaching to migrant pupils. 'The main need of migrant children is to learn English,' Rutter said. 'But funding of English language learning is just not keeping pace with the number of migrant children entering British schools. If we are not careful we are going to fail a generation of schoolchildren.'

Experts say the system for channelling additional funds to the more needy schools is flawed. Additional emergency funding is made available only if the number of pupils in a local authority region increases by 2.5 per cent or more. For somewhere like West Sussex, for example, this would require an overall increase of 2,275 pupils.

A spokesman for the Department of Children, Schools and Families pledged there would be a 'sustained' increase in funding for English language teaching, and that by 2010 the ethnic minority achievement grant would reach £206m.