The mix-up over results even showed that 89 pupils out of 90 had been absent when children at one school sat a maths paper.

This follows a national uproar after the exams were marked for the first time by the private firm ETS Europe, which has been awarded a five-year, £156 million contract by the Government.

Problems began last week when schools were told the results of the Key Stage 2 SATS, which are taken by 10 and 11-year-olds, would be delayed by a week. And when they did arrive, many schools began reporting major glitches.

In Peterborough, 10 schools awaiting Key Stage 2 results did not have all their papers for English tests returned, five schools did not receive all their maths results and two did not receive all their science results.

At Abbotsmede Community Primary School in Eastfield, Peterborough, errors were made in the marking of science tests which resulted in 10 per cent of pupils being given lower scores than they should have been.

Furious headteacher Brenda Wright said: "The children in year 6 have worked for the whole year to learn as much as they can for these tests.

"To not consider them important enough to make sure the system is correct is absolutely appalling.

"It is denigrating all the hard work the children have put in, and is just not appropriate."

Also unhappy is Margaret Sargent, headteacher at Alderman Jacobs Primary School in Whittlesey, where test results arrived a week later than promised – and when they were finally posted online they were riddled with howlers.

Mrs Sargent said they contained so many errors she was forced to keep them back from pupils

She said: "Lots of children were missing and the results website was showing children as absent when they had in fact taken the tests.

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"We had problems with English and problems with science, but the really bizarre thing was that out of 90 children who did one maths paper, it showed 89 were absent.

Mrs Sargent said scathingly: "It has been quite shambolic.

"As a teacher it is an appalling situation because the children worked very hard towards their SATS, but they have still not had their results.

"As a taxpayer, I have got some serious concerns about the company which is carrying out this operation and is being paid vast sums of money to do so."

Results for Key Stage 3 SATS were expected on Monday but are not due until at least next week.

The situation has also alarmed many parents whose children are set to chose vital options which will influence the future of their education.

One of them, Mr Kevin Banks (44), from Orton Malborne, says he is concerned his 14-year-old stepson, an Orton Longueville School pupil, will not get his results before the school closes on Wednesday.

He said: "They have no idea when we will receive them.

"It is a particular worry because he chose his options this year, and some of them will depend on the SATS results.