The head of Woodcote Junior School in Coulsdon, Croydon, has sent an invoice to Mr Blunkett charging pound;25 for every hour the school's assessment manager spent totalling the scores and calculating the levels.
The results of this year's tests for 11 and 14-year-olds were delayed because of blunders by the contractor employed to work them out.
Woodcote said it was forced to work out the conversions for 70 pupils to "meet parental expectations".
Teachers' leaders had earlier advised schools not to carry out the work, even though it would mean that parents did not receive their children's results by the end of the school year.
In a letter to the Secretary of State, the headteacher, Tony Pratchett, accused the Government, the Qualifications and Assessment Authority and the contractor Edexcel of a breach of contract and "failing to meet national undertakings".
Mr Pratchett said reimbursement would be a "very modest compensation" and added that any school making a similar blunder would have been publicly named and shamed by Ministers.
However, the QCA said this week it was under no obligation to pay for supply cover, and schools were not compelled to publish results until the end of September.
John Shield, senior media officer for the curriculum, said: "We have sent out two letters to schools, one informing them there would be a delay and the second telling them that we would send out the results by the end of August at the latest.
"We are not in a position to make payments."
A spokesman for the Department for Education and Employment said Mr Pratchett should have addressed his concerns to QCA. But he added; "The Government regrets the inconvenience caused by the late delivery of key stage 2 and 3 results by the QCA's national data collection agency. The QCA did take steps to keep the delay to a minimum. The Government took a close interest in the progress of this."