He told MPs that it would be hard to ensure that 85 per cent of 11-year-olds reached the achievement level for their age by 20062007.
Schools were originally aiming to reach the goal by this summer, but it was put back three years by the Government.
Mr Normington told the Commons public accounts committee that schools were set to fall "very significantly short" of the target this year.
Only around 75 per cent of primary pupils reached the expected levels for English and maths last summer.
The senior civil servant said that advances had been made up until 2001, but that results since then had reached a plateau. "We are having the greatest difficulty moving upwards," he said.