The table below show the badges listed in the 1937 Coronation Review of the Fleet at Spithead by HM King George VI on the 20th May 1937, but are known to have been in use earlier in the 1930's.
GUNNERY
Alma Mater - HMS Excellent - Whale Island, Portsmouth
The 1953 Review Programme showed a Gunnery badge like this, but went on to show these pictures.
The associated script read:- C.P.O., P.O., and confirmed Leading Ratings qualified as Gunnery, T and AS, Radar Plot, Wireless, Signalling Instructors and Staff Physical and Recreational Training Instructors wear a crown and two stars.
Letters indicating specialization within branches [but not qualifications]
Q Quarters
L Gunlayer
C Control
A Anti-Aircraft
R Radar Control
QA Quarters Armourer
CA Control Armourer
In the 1977 Review programme, again, just this one badge was shown but now renamed to MISSILE