The PA report by James Tapsfield said the SIA “admitted it had blundered again after a further glaring loophole was spotted in procedures”.
It said: “Thousands of three year licences have been issued to applicants, even though their right to work was due to expire within months.”
But a statement from the SIA said the PA report was “inaccurate”.
“The facts are misrepresented despite the Press Association being provided with a statement and full explanation. Representations have been made to Press Association.
“These routine checks demonstrate that our licensing system is robust and goes beyond our legal obligations.
“It is not true to say 1,350 illegal immigrants have slipped through the net. These individuals had previously been checked and had the right to work
“As part of our ongoing checks, we regularly review the status of licence holders who have time-limited permission to work.
“As part of those checks, we have identified a number of individuals whose right to work has apparently expired and we have taken the appropriate action.”
The PA report said: “Despite the errors, the SIA has said it rewarded top managers with nearly GB pound 50,000 in bonus payments last year.”
The SIA responded: “Regarding bonus payments, again, the figures again are misrepresented.”