The criticism follows a report by the Office for Standards in Education on a school in Bradford which claimed there were disadvantages in pupils regularly speaking Urdu to each other.
It said use of mother tongues by pupils at Belle Vue girls' upper school could help pupils explain difficult points to each other, but its regular use would restrict learning of English words and phrases. It said other pupils would be left out of discussions and teachers could not monitor progress.
The report on schools in the mainly Asian Manningham area, published last month, reflects concern in Bradford over poor examination performance and disaffection among young people from the ethnic minorities.
A separate report on the riots which broke out last year, mainly involving young Asians, also pointed to educational disadvantage in the community.
Upper school heads in Bradford, complain that many Asian pupils are being held back because of their poor grasp of English.
The city's education committee chairman, John Ryan, called for a public debate over changes of policy towards Asian schoolchildren.
"I believe that the council has in the past placed too much emphasis on the need for mother tongue teaching at the expense of English," he said.
"It is not a question of one or the other, it is about getting the balance right and improving standards of literacy and numeracy at an early age in all our schools."
Mr Ryan said the problem of children going on extended trips to their country of origin also needed to be tackled.
Alan Hall, headteacher of Belle Vue girls, who is drawing up the guidelines on use of Urdu in class as suggested by OFSTED, said: "In the past teachers have felt they would be labelled racist if they said a discussion in class ought to be in English.
"But we don't help the pupils if we don't make sure they have full command of the language. Obviously there is a place for the mother tongue, but the guidelines will say the medium of discussion should be English."
The city council has also said it will tighten up on conditions for its Pounds 30,000-a-year grant to "supplementary schools", often held in mosques, to encourage them to teach extra English and maths instead of Arabic and the Koran.
But Phil Barnett, principal officer for education at the Commission for Racial Equality, said: "Everyone would agree that it's absolutely essential for children to learn English so that they can play a full part in society.
"But a policy that says they should not speak their mother tongue in class is crude and unhelpful.
"Youngsters will not respect a system which makes such an unreasonable demand about how they should speak to each other. This takes the debate back about 20 years when such views were commonplace."