The Government said in October that the money to raise the achievement of these children would increase by 7 per cent next year.
But the National Union of Teachers claims that because of changes in the way the grant, formerly known as Section 11 funding, is calculated, most local councils will be forced to pay more.
If they took up their full allocation, they would have to take money from other parts of their education budgets.
For 2000-2001 the Ethnic Minority Traveller Achievement Grant has been allocated by a formula under which the Department for Education and Employment pays 58 per cent of the total with local authorities making up the remaining 42 per cent.
But the new system has thrown up winners and losers. DFEE contributions currently vary between local authorities, ranging from 45 to 65 per cent.
For example, Birmingham's allocation goes up from pound;5.91 million to pound;7.29m - a 23 per cent rise, according to NUT figures. But, because the percentage paid by the Government has fallen from 65 to 58 per cent, Birmingham's contribution has jumped from pound;2.07m to pound;3.06m - a 48 per cent rise.
Coventry's total grant remains the same, at around pound;3.21m. But it must find an extra pound;225,000 to achieve the same level of spending next year.
However, there are winners, including the London borough of Greenwich - where the total grant is slightly up but the borough's contribution is down.
John Bangs, the NUT's education and equal opportunities officer, welcomed the increase in the grant and the Government's attempt to rationalise a system previously based on bidding and historical patterns of funding.
But he said there was not enough money to go around, and it was being spread too thinly.
Doug McAvoy, the union's general secretary, accused the Government of operating by deceit.
A spokesman for the DFEE said the new grant of 58 per cent was expected to continue next year - and was more generous than the 50 per cent matched funding contributed towards most other grants from the Standards Fund.
He added: "It's not fair to expect education authorities with the same level of need to be paying different amounts (as under the previous grant system)."
In addition to the traditional support for children with English as another language, schools and authorities are having to look again at curriculum content and pupil exclusions.
The scrutiny reflects the Government's inclusion policies and the recommendations of the inquiry into the murder of black teenager Stephen Lawrence.