The Education Secretary has written to local authorities urging them to reconsider their budgets for next year.
But the action - believed to have no legal standing - provoked anger from social services departments who say he has exceeded his powers.
Now Mr Blunkett has told councils to ensure all the cash increase in education standard spending assessments is spent on education services as the Government intends.
In response, Chris Davies, president of the Association of Directors of Social Services, said: "All local authorities recognise the importance of education spending. However David Blunkett does seem to be going beyond his remit."
Several of the authorities to receive the letter are already spending above SSA - the level that the Government believes necessary for education. Others had faced cuts in the social services grant for children in care.
And said Mr Davies: "For some authorities, the only way they could put more into education next year would be by cutting back on their other big area of spending which is social services.
"Should local authorities now be expecting a similar letter from Frank Dobson, the Health Secretary? Where would all this stop?" The 18 councils which were sent letters are Brent, Bristol, Cambridgeshire, Cumbria, Dorset, Hackney, Hertfordshire, Lancashire, Leicestershire, Lincolnshire, Norfolk, Redbridge, Somerset, South Gloucestershire, Walsall, Waltham Forest, West Sussex and Wiltshire.
Analysts suggest the Government is under great pressure to pump extra money into schools from April so that it can meet its pledge to cut infant class sizes to 30 or fewer pupils.