Tower Hamlets, Oldham and Kirklees councils are among those frustrated by what one education chairman described as "Whitehall dithering".
Education authorities receive the bulk of the money towards specialist English teaching from the Home Office's Section 11 fund and the Department of the Environment's Single Regeneration Budget (SRB).
But with most Section 11 funding (worth Pounds 58.8 million in 1996-97) due to dry up next March, they want the Government to tell them if and how that money will be replaced.
They say the current situation has made it impossible to plan ahead.
Tower Hamlets education chairman Michael Keating said councils had been left "groping around in the dark" over Section 11.
"This is Whitehall dithering. It appears that the Department for Education and Employment, Home Office and Government Office for London cannot agree who is responsible for continuing with the initiative and how much money, if any, will be available," Mr Keating said.
He added that the council was originally told it would know by Christmas 1995 if and how Section 11 funding, which currently pays for 300 teachers assisting about 30,000 of the borough's 36,000 pupils, would continue.
But subsequent representation and letters to Education Secretary Gillian Shephard and Home Secretary Michael Howard, some of them made in association with Oldham and Kirklees councils, had failed to produce a definite response.
Mr Keating said: "We don't mind where the money comes from, just so long as we know we will have it and be able to continue the good work. At the moment, the uncertainty is making it impossible for us to make any short - or long-term - plans for assisting pupils who need help with their English."
Tower Hamlets recently submitted a Pounds 19m SRB bid as "an insurance policy" against the loss of Section 11 funds.
A spokesman for Oldham council, which employs 116 teachers to work with 7,000 bilingual pupils, said: "We're continuing to lobby the Government to make a favourable decision on the Section 11 issue, which is creating a great deal of uncertainty in the minds of English language teachers."
Hundreds of teachers have lost their jobs as a result of Government cuts in Section 11, down by more than 50 per cent, from Pounds 130m in 1993-94.
A Home Office spokesman said: "Ministers are conscious that authorities are anxious to know how they stand.
"They hope to be in a position to let them have more information shortly. "
In March, Doug McAvoy, general secretary of the National Union of Teachers, criticised the "damaging divisions and temporary allocations" of the current arrangements and said the teaching of bilingual pupils should be made the sole responsibility of the DFEE.