The poll also found that a quarter of parents did not know the letters even existed. But parents are supportive of school inspections, with more than 90 per cent believing they were a good idea and over 80 per cent saying inspections had led to improvements.
In a separate survey in July, some headteachers criticised inspectors'
letters for undermining staff morale and, although most pupils thought the letters were a good idea, some found their tone patronising.
Miriam Rosen, Ofsted's director of education, said more needed to be done for the letters to win wider support. "We are never complacent and there is clearly still work to be done to prove the worth of the letter to pupils,"
she said."When we published a survey of headteachers' and pupils' views of the letter we said we would offer more advice to inspectors about appropriate styles of writing for different age groups, and we have done this."
Ms Rosen welcomed the survey's findings of parental support for inspections, with only four per cent saying they were not in favour.
Eighty-one per cent said shorter-notice inspections, where schools learn of inspections only a few days in advance, were a good idea, with 14 per cent against them. Chris Keates, general secretary of the NASUWT, said: "The only reason Ofsted conducts surveys is to pose questions which will elicit responses it can use to justify its own existence.
"Can there be anyone who is surprised that the majority of parents want schools inspected? Such a response cannot be used to support the continuation of the present inspection regime."
The survey results are based on 510 interviews with parents, conducted by Ipsos MORI.