Mr Blunkett 'named and shamed' the council last week, claiming it had held back part of an extra£3.8 million given for education in 2000-01.
The council bitterly disputed the accusation and complained that civil servants had blundered over the figures (LGC, 25 February).
Stockton said it was being punished for ploughing an extra£1.6m into education in 1999-2000, thanks to a one-off windfall from a business rates rebate. Civil servants mistakenly viewed the£1.6m as part of the council's base budget for education, which made it look as though it was only passporting£2.2m of the£3.8m.
In a letter to leader Bob Gibson, Mr Blunkett said: 'Having studied the figures further, it is clear the net effect is that the comprehensive spending review uplift for 1999-2001 has reached schools. I look forward to your continued support for education in Stockton-on-Tees and for our policies to raise standards.'
The council immediately declared itself 'unnamed and unashamed'.
Mr Gibson said: 'The DfEE had got this one wrong but to its credit it's come clean and acknowledged it. We were shocked by the claim that we would do anything other than spend extra education money on education.'
Mr Blunkett has attacked seven other councils for allegedly failing to pass on extra education funding: Somerset CC (granted an extra£10m), Newcastle upon Tyne (£3m), Solihull MBC (£4m), Kensington & Chelsea LBC (£3m), Hillingdon LBC (£7m), Westminster City Council (£4m) and Shropshire CC (£4m). The DfEE said the education secretary intended to keep up the pressure on these councils and the Stockton case was a one-off.