The booksellers claim they are unable to provide schools with the books they need for the tests at key stage 1 because they and the publishers have not been given sufficient notice of SCAA's list of books for the national tests. Also, up to one-third of this year's list is out of print.
Fay Sinai, who works for Blackwell's Children's Bookshop in Oxford and chairs the children's group of the Booksellers Association, said SCAA was failing to take notice of the "absolute furore" the lists were causing among booksellers and teachers. She said: "I cannot get hold of a lot of these books in bulk. I service schools and I haven't been able to supply one of them with all the books requested."
Although teachers are required by SCAA this year to make sure books used for assessment "are not familiar to the children", the shortage in bookshops has been exacerbated by the fact that The Red House, a book club which promotes itself through schools, bought in bulk early from publishers and has been actively selling books from the tests list to parents, running a "buy-two-and-get-one-free" promotion for some titles.
Many of the listed books are classics - such as Mr Gumpy's Outing by John Burningham, Kipper by Mick Inkpen and All In One Piece by Jill Murphy - and can already be found in many homes and libraries.
Although the list is a public document, SCAA is alarmed that it has been promoted to parents and is anxious that children should not be drilled in the texts before the tests.
Fay Sinai said: "Parents know the list and they are ordering the books. We cannot keep up with the demand. Children's picture books are especially expensive to reprint and publishers are not prepared to commit themselves until they know what the sales figures are going to be. They will not reprint just on say-so.
"We cannot give them accurate figures because we do not have the books to meet demand. This is a real Catch 22. We are talking to SCAA but getting nowhere fast."
The dispute has intensified this year because SCAA has changed the book list substantially, requiring for the first time that the books should not be familiar to children. This is in response to teachers' fears that some children were gaining an unfair advantage because they were being coached with the texts.
Although SCAA's attempts to use real books to test children's reading have met with approval, publishers say it can take up to three months to reprint a book and are pressing the curriculum advisers to communicate better and issue the list earlier.
"We have had difficulties since SATs began," said Philippa Dickinson, children's publisher at Transworld and chair of the children's book group of the Publishers Association.
"Booksellers are deeply frustrated because they cannot supply teachers with all the books they need, but it is very difficult for us to anticipate demand."
SCAA argues that it does consult publishers beforehand, and places books on the list only if it is assured that they will be kept in print. "Many publishers are surprised to find they have said yes to this," Ms Dickinson said. Last week SCAA leaned heavily on The Red House to cease its "very regrettable" promotion of the lists to parents.
The book club has apologised to SCAA and agreed not to promote books as assessment texts in future, a spokesman said.
David Hawker, SCAA's assistant chief executive for statutory assessment for five to 14-year-olds, said: "We rely on booksellers to exercise restraint when they know books are used for national assessment. Teachers are contacting us because they believe the task is being undermined. We are very keen that parents should help children with their reading, but to coach children with these texts beforehand is not helpful for the assessment."
Mr Hawker is to meet with booksellers soon to attempt to settle the supply dispute but believes The Red House's promotion may have exacerbated shortages. He said: "We let bookshops have the list one month before the schools, which are informed in November. We contacted publishers in July, but some of them appear to have miscalculated what the demand would be."
He believed it was in publishers' and booksellers' interests to maintain supplies so that SCAA could keep up its real books policy. SCAA, he said, did not want to be forced down the road of producing an anthology of unseen passages for this kind of assessment for seven-year-olds.