Home Office minister Timothy Kirkhope this week told local authority leaders that the Section 11 scheme, used to pay for extra teachers and classroom assistants, would continue for another year, but a decision was yet to be made on how much cash it would involve.
The Association of County Councils and Association of Metropolitan Authorities complain that they have been pressing for more than two years for a decision on the future of the money, due to run out in March.
The National Union of Teachers, which met Mr Kirkhope separately, was jubilant that the scheme was to continue, but warned that current spending levels should be maintained.
The associations fear that up to 8,000 jobs could be lost and race relations damaged if a decision is not made quickly. They want the funding renewed for a further year.
Responsibility for some cash used to pay for teachers and classroom assistants - themselves mostly from ethnic minorities - has been transferred to the Department of the Environment under the single regeneration budget.
But no decision has yet been made over who will be responsible for the major part of the funding, paid to local authorities by the Home Office.
Graham Lane, AMA education committee chair, who jointly led the delegation to the Home Office this week, said: "There will be many staff made redundant if we don't get this funding. It's the height of irresponsibility by the Government. It shows a lack of commitment to race relations. No other group of people would be treated like this.
"The needs in this area are increasing, but the Government does not seem to understand that there will always be children in our schools who need extra help."
John Bangs, education officer at the NUT, said: "The fact that the Government has said for the first time that Section 11 will continue is a big step forward. But we will be extremely angry if the funding for a further year is reduced."