Sir John complained that 60 of 172 local education authorities had failed to do so by the 31 December 2001 deadline and 465 audited returns from other employers had by then not been received.
The missing paperwork covers £644m in contributions.
Bourn said he qualified his opinion because managers of the scheme were unable to provide him with sufficient evidence to support the completeness and accuracy of contributions received and because he had been unable to reach an opinion that contributions had been received in accordance with scheme rules and the recommendations of the actuary.
But he said that even if the evidence had been available, contributions may have needed adjustment in the light of audited information received.
Alternative arrangements existed for confirming length of service and the pensionable salary of teachers, reducing the risk that their benefits would be based on incorrect information, he said
Bourn said managers were reviewing the way they verify completeness and accuracy of contributions from employers and may, in future, recommend alternative methods of gathering membership and other key data.
In 2000/2001 the scheme disbursed some £3.58bn in retirement and other benefits and collected £2.01bn in contributions.
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