The move comes after widespread cheating was discovered at test centres in a BBC London/Newsnight investigation.
Hidden camera filming exposed the systematic cheating which allowed untrained builders on to dangerous sites.
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Five testing centres have now been closed and a further eight are under investigation. CCTV is also being installed in all test centres, while stop checks are to be stepped up.
Carl Rhymer, Director of Delivery and Customer Engagment for CITB, said: "Following analysis of how the test was answered, using known testing patterns and geographical factors, we will require 6,000 individuals to be retested.
"Many of these are expected to be legitimate, but this is to eliminate any doubt."
(LM/CD)
