It would appear that the school OTC wore the blackened badge and it was the CCF that wore the brass version. EJ Martin's article does not specify which one was in use in '38. The School's archive suggests that the black badge was in use by the Cadet Corps 1915-23, and then by the OTC 1923 into the 30's and 40's. The brass one was in use in the 50's. Later replaced by the Queen's badge in the 70's and then PWRR.
http://www.alleyns.org.uk/alleyn/Alu...okletfinal.pdf