The National Association of Head Teachers and the National Union of Teachers told a House of Lords committee that they did not have the money needed to help the large numbers who did not speak English, although they praised the pupils' hard work.
Steve Sinnott, NUT general secretary, said: "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 can speak English."
The equality and Human Rights Commission suggested that good schools should limit the number of middle-class pupils they admit.
Trevor Phillips, chairman of the watchdog, told a conference in London on community cohesion that he wanted top schools to place quotas on middle-class pupils in order to ensure that more children from poor homes have access to good education. He said that spreading poorer pupils evenly across different schools had helped tackle class divides in the United States.
Government figures showed that black pupils are catching up on their white classmates at GCSE.
This year's exam results show the number of black African and Afro-Caribbean boys achieving five A-star to C grades has risen at twice the rate of the national average.
Poorer children are still underperforming. Only 35 per cent of children eligible for free school meals achieve five good GCSEs, compared with 63 per cent of others.
A study of parents with children in independent schools found that many were spending nearly half their incomes on school fees.
The report by MTM Consulting suggested that one in six of the 900 parents surveyed devoted 40 per cent or more of their net income towards fees. Some had taken second jobs or remortgaged their homes.
The liberal Democrats obtained figures showing that the Government's education advisers and ministers spent pound;4 million in first-class rail travel last year.
Describing the expenditure as "astonishing", the Sunday Express calculated that the money spent on travel for Department for Children, Schools and Families staff would pay the salaries of 200 teachers, each earning pound;20,133. Alternatively, it would pay for 115 headteachers, each on a salary of pound;34,938.
A British primary teacher in Sudan was arrested for naming a teddy bear Muhammed. Gillian Gibbons, 54, faced 40 lashes or up to six months' in prison after being accused of insulting Islam's prophet. Pupils voted for the name and had taken turns filling in a diary for it, headed "My Name is Muhammed".