By putting "its eggs into one target basket" the Government is penalising primary schools in deprived areas, according to the National Association for Primary Education.
The association insists that the bottom-line national target that 80 per cent of 11-year-olds should reach reading level 4 by 2002 is particularly unfair to those "schools tackling severe social and economic disadvantage".
John Coe, its information officer, said: "In order to reach the targets these schools are going to have to work twice as hard.
"At present schools in poor areas are reaching about 35 per cent at level 4, that means doubling standards in order to hit the target.
"Schools in non-deprived areas are already averaging 55 per cent at level 4: that means they only have to make a 25 per cent improvement.
"No one wishes to be seen to be afraid of targets, but they've got to be realistic. The Government seem to be blindly ignoring a child's background and factors over which a school has no control."
Last month Stephen Byers, the school standards minister, unveiled individual targets for every local education authority, based on their existing levels of achievement in English.
However, no individual authority will be allowed to set a target of less than 70 per cent.
Mr Byers said the "old approach" of blaming poverty and social disadvantage for under-performance would not be tolerated.
John Coe believes this will result in children at the "bottom end of the achievement spectrum" being neglected.
He said: "Heads under pressure would be forgiven for putting their best teachers and most effort into those children most able to improve quickly. But what about those low achievers, the 30 per cent? We believe they are the greatest educational problem we have in the UK today. There are no targets to help them."
Alan Wells, director of the Basic Skills Agency, does not think the targets are generally unfair.
He said: "The individual targets are for authorities, not schools. I'm sure authorities are going to recognise the vast differences in their own schools accordingly.
"Some of the improvements already successful schools have got to make are going to be just as tough as those for schools in poorer areas.
"I know of one authority that was already at 67 per cent, so they've been given a new individual target of almost 90 per cent. To be fair, everyone is going to work as hard on this one."