The seven, known collectively as the E7 - an ironic twist on the notion of the G7 richest nations - held an inaugural meeting in Warwickshire last week to discuss the restrictive increase in the "cap" of 0.5 per cent.
At the same time the teacher's pay award was set at 2.7 per cent and inflation is running at around 3.4 per cent.
The seven authorities - Staffordshire, Northumberland, Hereford and Worcester, Derbyshire, North Yorkshire, Suffolk and Warwickshire - are among the poorest in England and are at the bottom of the league tables for SSA spending per pupil.
Representatives from only seven authorities were invited to the initial meeting to emphasise the G7 concept - although membership is open to any LEA wishing to join.
Worst off is Staffordshire which, according to Department for Education figures, spends Pounds 2,398 per secondary pupil and Pounds 1,805 per primary pupil, compared with the highest spender Surrey on Pounds 2,679 and Pounds 2,010.
Cheshire, which is third from bottom in the secondary list and second from bottom in the primary, is also likely to join the E7.
The seven authorities between them have to make savings of almost Pounds 70 million and up to 1,000 teaching jobs could go in order to balance the books.
John Airey, Warwickshire's education committee chairman, said: "What we are doing is similar to what the parent power nationwide is striving to achieve. I believe that we should pull together to urge the Government to rethink the disastrous spending limits it has imposed on authorities.
"There is speculation that money is to be pumped into the Autumn Statement that is too late for many of our children who stand condemned by the Government's failure to act.
"I challenge the Chancellor to come to each to each of these authorities with his team of experts and examine our books and tell us how we can manage within the current unfair funding system."
Of the E7 authorities, Derbyshire has the biggest financial problems. The county has had to make savings of Pounds 20 million to its education budget, resulting in a Pounds 12.2 million reduction in schools' spending.
Predicted job losses include up to 150 full-time and 250 temporary teaching jobs and a further 400 are expected to be lost from other areas as a direct result of the cost-cutting measures.