Authorities are failing to investigate properly allegations of cheating in which pupils say they were given answers to Sats questions by teaching staff, it was claimed this week.

The TES has spoken to pupils at a south London primary - which cannot be named for legal reasons - who claim staff, including an executive head, in effect told them what to write as they sat a series of national tests.

At least three parents have contacted the Qualifications and Curriculum Authority about the case but say the watchdog has failed to follow up their calls or speak to pupils to gather the details they would need to conduct a proper investigation.

The authority says it is investigating “alleged maladministration” at the school. But The TES has seen copies of an email exchange that appears to confirm that the QCA has not taken at least one breach of the rules seriously.

Some allegations of schools cheating in Sats can be investigated forensically by checking question papers for tampering. But in this case, parents say, the only way the truth can be uncovered is by speaking to the pupils. An 11-year-old boy at the anonymous school said his head and deputy head looked at papers in a science test before they were handed in and told pupils to reconsider some answers.

“They said, ‘Look at that again - it’s wrong. Check the answer - it’s not correct. Think again,’ ” he said. “They kept on saying it until we got it right.”

In an English spelling test, words were sounded out very slowly.

“They basically spelt the words for us,” the pupil said. He said he was also told the answers to multiple-choice questions in a maths test.

The pupil said school staff altered their behaviour and did not speak during tests when outside observers were present.

His stories are backed up by a 10-year-old classmate, interviewed separately, who said his head came over when he could see he was having trouble. “Sometimes, if I already had an answer, he would come over and say, ‘Think about it. Use your brain,’ ” he said.

A girl at the same school was off sick for the first three days of Sats week. On her return, she was greeted by pupils saying: “The Sats are so easy. (The deputy head) is telling us all the answers.”

She then sat a maths test in which every pupil in the room had a dedicated teaching assistant looking over their shoulders and watching what they wrote.

“If I put an answer down, she would nod her head if I got it right and say, ‘Yes, well done,’ ” the pupil said. “If I got it wrong, she would be like, ‘No, try again. Think about it properly.’”

Sometimes the teaching assistant actually gave the answer, she said.

The girl’s parents were not told by the school that she took two English tests late when she returned. QCA rules say this must only happen where schools can confirm that the pupil has not had contact with other pupils who have already sat the test, and where parents take responsibility for this lack of contact outside school.

But the girl’s mother said: “Nobody from the school rang us. Nobody told us anything.”

When her husband reported this breach of the rules to the QCA, an email shows that the “test administration manager” who replied failed even to acknowledge the allegation.

A QCA spokesman would say only that the case was being investigated and that parents would only find out the result if test marks were altered, in which case the school would have a duty to tell them.

Last year, the authority looked into 503 cases of possible test “maladministration”. But results were changed or annulled in just 70 schools, and in 41 of those cases it was because the school had reported pupil cheating.